Arbitrary Lagrangian Eulerian Framework Research Articles

A high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for one-dimensional compressible multi-material flows

In this paper, a high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian (ALE) discontinuous Galerkin scheme is proposed for one-dimensional compressible multi-material flows. Our scheme couples a conservative equation related to the volume-fraction model with the Euler equations for describing the dynamics of fluid mixture. The mesh velocity in the ALE framework is obtained by using an adaptive mesh method that can automatically concentrate the mesh nodes near the regions with large gradient values and greatly reduce the numerical dissipation near material interfaces. Using this adaptive mesh, the resolution of solution near some special regions such as material interfaces can be improved effectively by our scheme. With the appropriate time step condition and using a bound-preserving and positivity-preserving limiter, our scheme can ensure the positivity of density and pressure and the boundness of volume-fraction, which further ensures the computational robustness and degree of confidence of simulations under large density or pressure ratios and so on. In general, our scheme can be applied to the simulations of compressible multi-material flows efficiently with the essentially non-oscillatory property and physical-constraints-preserving (bound-preserving and positivity-preserving) property, and its steps are more concise compared to some other methods such as the indirect ALE methods. Some examples are tested to demonstrate the accuracy, essentially non-oscillatory property and physical-constraints-preserving property of our scheme.

Ambient-gas forced convection dictated evaporation kinetics of generic sessile droplets

We probe the temporal evolution of internal thermo-hydrodynamic features of evaporating sessile droplets under external forced convection. A transient numerical model based on Arbitrary Lagrangian-Eulerian (ALE) framework is adopted. The governing equations corresponding to the transport phenomena (mass, momentum and energy) are solved in a fully coupled manner in both the droplet (liquid) and ambient (gaseous) domains while accurately tracing the droplet interface evolution. The role of initial wetting state, external convection velocity and convective heating/cooling effects due to the air-flow are explored in details, and good agreements are noted with previous reports from literature. Results show that although the evaporation rate is augmented significantly in forced convection conditions, the same does not increase in proportion at higher Reynolds numbers. This is primarily due to the enhanced cooling effects that reduce saturated vapor concentration at droplet surface, and thereby supress the diffusion mechanism. Also, depending upon the contact angle, the evaporative cooling effects are compensated partially or completely due to convective heating. This altered thermal profile substantially influences internal hydrodynamic features (Marangoni flow and heat advection) during the transient and stable regimes of droplet evaporation. At higher degrees of convective heating, the droplet interface temperature becomes higher than its base temperature. This condition results in a completely opposite internal Marangoni vortex at stable state compared to that induced due to evaporative cooling effects. We also provide a regime map to show the role of the gas-phase Stefan number on the droplet-phase hydrodynamic regimes.

Mixed convective heat transfer in a square cavity filled with power‐law fluids under active flow modulation

AbstractThe current study presents a computational investigation of mixed convective heat transfer in a square enclosure containing power‐law fluid. An active flow modulator is employed in the form of a flat plate with negligible thickness, and the mixed convection is achieved through clockwise rotation of the plate. The rotation of the plate is modeled by incorporating a moving mesh technique. The solution is then obtained by applying the Finite Element Technique under the arbitrary Lagrangian–Eulerian framework. Numerical validation is performed with contemporary research studies consisting of rotating plates to justify the accuracy of the present study. The study is conducted at constant Prandtl number Pr = 1.0 and Reynolds number Re = 500 while varying the power‐law index (0.6 ≤ n ≤ 1.4) and the Richardson number (0.1 ≤ Ri ≤ 10.0). The results have been presented in terms of the flow and thermal fields, spatially averaged Nusselt number, spatially averaged power consumption by the plate, and the velocity and temperature profile in the enclosure. The numerical findings indicate that a higher Richardson number encourages heat transfer. For the shear‐thinning fluid, a 37% thermal augmentation is observed in comparison to the Newtonian fluid at Ri = 10. However, in the case of shear‐thickening fluid, thermal performance was reduced by 21.13%. Small thermal oscillations are observed in naturally dominated mixed convection for shear‐thinning fluids, but none are observed for shear‐thickening or Newtonian fluids. In addition, the findings demonstrate that the flow modulator has a positive impact on heat transfer for the shear‐thickening fluids (n > 1) and an adverse effect for the shear‐thinning fluids (n < 1). Furthermore, the power consumption decreases as Ri increases, and it becomes negative beyond Ri = 1.0 due to the increase in natural convection strength.

An arbitrary Lagrangian–Eulerian positivity-preserving finite volume scheme for radiation hydrodynamics equations in the equilibrium-diffusion limit

In this paper, an arbitrary Lagrangian–Eulerian (ALE) positivity-preserving finite volume scheme is constructed for radiation hydrodynamics equations (RHE) in the equilibrium-diffusion limit. Firstly, the integral form equations of RHE in the ALE framework are presented. Then, the operator-splitting method is applied to divide the equations into hyperbolic part and parabolic part. In addition, a second-order positivity-preserving finite volume scheme is constructed for the hyperbolic part based on MUSCL reconstruction. The vertex velocity is obtained by the predictor–corrector strategy. The Winslow method is applied to improve the quality of the Lagrangian mesh. Furthermore, a nonlinear positivity-preserving finite volume scheme suitable for distorted mesh is proposed for the parabolic part. Finally, some numerical examples are given to show the accuracy and reliability of the numerical scheme.

Numerical modeling of systems based on SMA wires and pulleys: A finite element formulation within the Arbitrary Lagrangian–Eulerian framework

Thanks to their properties of superelasticity and shape memory effects, SMA wires are often considered for the design of damping devices or actuators coupled to pulleys. In order to dimension such devices for commercialization, it is necessary to develop reliable, robust and fast numerical tools. To this end, simplifying the management of the wire/pulley contact using an Arbitrary Lagrangian–Eulerian (ALE) formulation is an original and effective solution. In this work, the wires are modeled by three-dimensional truss thermo-mechanical finite elements associated with a superelastic law. For each node, the curvilinear abscissa is used as an additional degree of freedom in order to deal with material flow from one element to another. After presenting the ALE formalism and the necessary precautions (advection of variables), as well as the material behavior and thermo-mechanical contact laws at the pulleys, elementary validation tests are studied. Finally, two devices taken from the literature are modeled using the ALE formalism. The results obtained demonstrate the relevance and effectiveness of the approach adopted, as well as the importance of not neglecting friction at the pulleys and thermal effects on the material mechanical response.

Nonlinear vibration and acoustic radiation of an internally resonant buckled beam

Although the nonlinear vibration of buckled beam has been thoroughly studied, its acoustic radiation does not get much attention. This paper deals with the nonlinear vibro-acoustic problem of an internally resonant buckled beam immersed in an infinite fluid. A finite element method based on an arbitrary Lagrangian-Eulerian framework is adopted to analyze the nonlinear interaction between the large-deformed buckled beam and the finite-amplitude acoustic waves in the fluid. The effects of acoustic pressure excitation, external harmonic excitation, and internal resonance on the vibro-acoustic responses of the buckled beam are discussed in the first and second primary resonances. It is found that the amplitude of the acoustic pressure can be comparable to the amplitude of the external harmonic force. This leads to an increase in the critical harmonic excitation amplitude for the occurrence of quasi-periodic responses and an increase in the second mode frequency component of quasi-periodic responses compared to the case neglecting the acoustic pressure excitation on the beam. Saturation phenomena are discovered in the second mode frequency components of beam displacement and acoustic pressure. Due to the 2:1 internal resonance, different time-frequency characteristics, quadrupole acoustic directivity patterns with low radiation efficiency, and dipole acoustic directivity patterns with high radiation efficiency can be observed at different harmonic excitation amplitudes and frequencies. Understanding these phenomena will help design loudspeakers and recognize sound sources.

Mixed convection characteristics in a long horizontal lid‐driven channel with periodically distributed local flow modulators

AbstractThis study explores the effectiveness of periodically placed rotating blades in enhancing heat transfer in a channel. The channel consists of a cold top plate moving at a constant speed and a fixed hot plate at the bottom. Thin rotating blades are placed periodically along the channel's centerline, with the spacing between their axes equal to the channel's height. This paper analyzes a transient, two‐dimensional, laminar flow problem using energy, momentum, and continuity equations. To address the challenges posed by moving blades, the Galerkin finite element method is implemented within an arbitrary Lagrangian–Eulerian framework, employing a triangular mesh discretization scheme. This study comprehensively explores thermal and hydrodynamic characteristics, including overall heat transfer, thermal frequency, and power consumption of the rotating blade for heat transfer in mixed convection scenarios with Richardson numbers (Ri) ranging from 0.1 to 10 at varying rotational frequency of the blade. Outcomes demonstrate that the inclusion of a rotating blade increases heat transfer up to 50% at lower Ri, after which the impact of the rotating blade diminishes and heat transfer reduces up to 20% at higher Ri. In addition, heat transfer enhances with increasing blade frequency up to Ri = 6.5, beyond which the effect of the frequency overturns. Examining thermal and hydrodynamic characteristics reveals that the blade achieves optimal performance when operating at f = 1 and Ri = 3. The study's insights into mixed convection heat transfer offer versatile applications, benefiting industries and equipment such as electronic cooling, chemical reactors, food processing, material fabrication, solar collectors, and nuclear reactor systems. Moreover, the findings are instrumental in the thermal ventilation of buildings and the development of micro‐electromechanical systems.

Fluid-structure interaction induced mixed convection characteristics in a lid-driven square cavity with non-Newtonian power law fluids

The present study aims to numerically explore Fluid-Structure Interaction (FSI) induced mixed convection characteristics in a square cavity filled with a non-Newtonian power-law fluid. The side walls of the cavity under consideration are subjected to constant low temperature having motion in opposite directions while the insulated top wall and the bottom hot wall are kept stationary. A flexible fin is mounted on the bottom wall that essentially serves as a passive flow modulator. To solve the transient flow, thermal, and stress fields, the FSI problem is presented in an arbitrary Lagrangian-Eulerian framework employing the Galerkin finite element method. Different non-Newtonian fluids are represented by the power-law index (n) varied within the range, of 0.6 ≤ n≤ 1.4. Besides, the dynamic as well as mixed convection condition of the flow is analyzed by variation of Reynolds number (100 ≤ Re ≤ 300) and Richardson number (0.1 ≤ Ri ≤ 10.0) respectively. System characteristics have been evaluated in terms of streamline and isotherm contours, spatial and time-averaged Nusselt number as well as Normalized Nusselt number in regard to the “No Fin” case. The outcome of the present study reveals that the efficacy of a flexible fin for a given system depends on both the system dynamic condition (Re) and the mixed convection regime (Ri). The presence of a flexible fin has been found to have positive impact on heat transfer performance for both the shear-thinning and shear-thickening fluids for higher values of Re and Ri. However, for lower values of Re, the inclusion of a flexible fin has been found to adversely affect the heat transfer performance for shear-thickening fluids. Moreover, the thermal field exhibits periodic oscillation properties at Ri = 10, which can be attributed to the induced motion of the flexible fin. This phenomenon has been further elucidated through Power Spectrum Analysis. Results obtained in the present study might provide valuable insights into FSI-induced mixed convection with non-Newtonian fluids having versatile industrial applications such as solar thermal collectors with strategically positioned passive flexible flow modulators.

Liquefaction-induced large deformation method with automatic time-step mapping and interfacial interpolation improvement: Case study of the San Fernando dam

This study constructed the u-p equation for saturated soil in the meshfree global weak form within the arbitrary Lagrangian-Eulerian (ALE) framework to solve the problem of liquefaction-induced large deformation induced by strong seismic loading. The interpolation improvement in the near-interface zone was achieved using domain truncation optimization and the local nodal refinement algorithm, and the relative error of the shape function was proposed as the judgment criterion for radial basis function (RBF) field variable mapping. Finally, a high precision meshfree liquefaction-induced large deformation method (MFLLDM) with automatic time step mapping and interfacial zone interpolation improvement was established. The MFLLDM achieved the efficient dynamic updating of soil stress state and pore pressure information in space during the deformation process and more accurately depicted the localized large shear deformation characteristics of the soil in the near-interface zone. The proposed method was integrated into a custom-built large-scale finite element method (FEM) computing system (GEODYNA), based on object-oriented and super element program design technology. This enabled the efficient coupled analysis of MFLLDM in the liquefied-induced large deformation zone and FEM in the small deformation zone. Numerical consolidation examples were used to validate the accuracy, convergence, and applicability of the soil elasto-plastic model for MFLLDM. The method was then used to simulate the liquefaction damage of the San Fernando dam, which reproduced the development process of large slip deformation and high-water pressure ratio for the upstream dam slope.

Droplet evaporation on curved surfaces: transients of internal and external transport phenomena

We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection due to bulk fluid motion. This bulk motion in the liquid domain is caused by natural advection due to thermal actuations such as thermal Marangoni flow and buoyancy-driven convection. For the gaseous domain, the additional effects of solutal convection (due to vapour-concentration variation), Stefan flow and interfacial viscous stresses are also considered. To depict a generalized role of substrate curvature, both concave and convex surfaces with curvatures over a wide range are studied. The surface wettability effects are also explored by varying the true contact angle of the droplets. Computational predictions on evaporation rate and internal flow field are validated against experimental results from literature. The interplay of wetting state and substrate curvature is noted to substantially affect the evaporation process and its thermo-fluidics. The convex curvature significantly augments internal advection while the same is weakened over concave substrates due to altered mass loss rate. Consequently, the duration of multi-vortex Marangoni flows in the development stages of evaporation and the advection in the external gaseous domain is markedly different for different curvatures. Further, on superhydrophobic curved surfaces, the effects of re-distributed evaporative fluxes play a major role. In such cases, the reduced mass flux over a large interfacial area near the periphery expedites the stable state Marangoni and external flow features.

Comparative study of WCSPH, EISPH and explicit incompressible-compressible SPH (EICSPH) for multi-phase flow with high density difference

This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian–Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and reformulated in the ALE framework. The Explicit Incompressible-Compressible SPH (EICSPH) method, which can handle both compressible and incompressible phases, is developed by combining these two approaches in a fully explicit algorithm. The proposed methods are validated and compared through four benchmark problems including Rayleigh-Taylor instability, hydrostatic, liquid sloshing and dam break problems. Firstly, the stability and accuracy of interface modeling of the three methods were verified through Rayleigh-Taylor instability with small density differences. In the hydrostatic problem with a large density difference, the results from all three methods exhibit good agreement in the pressure distribution. Particularly, EICSPH demonstrates the faster convergence when compared to WCSPH, with EISPH showing fastest convergence overall. In the transient sloshing problem, all three methods quantitatively converged to the experimental results and exhibited good agreement, although slight pressure noise was observed in WCSPH initially. Finally, in the dam break problem, all three methods successfully simulated sharp interfaces without non-physical voids. The temporal variations of pressure and height were well predicted by all three methods, with EISPH showing better conformity to the water-air interface morphology obtained from other incompressible numerical methods compared to WCSPH and EICSPH. Additionally, the impact of air speed of sound was examined in EICSPH, where while the difference in pressure variation at the probe was minimal, differences were observed in energy dissipation and the progression of the free surface due to the air cushion effect.

External Stefan and Internal Marangoni Thermo-Fluid Dynamics for Evaporating Capillary Bridges.

We probe the evaporation mechanisms of wettability-moderated, confined capillary bridges and bulges. For the first time, we explore the internal Marangoni hydrodynamics and external Stefan advection dynamics in the surrounding gaseous domain due to evaporative effects. A transient simulation approach based on the level set (LS) method and the Arbitrary Lagrangian-Eulerian (ALE) framework was adopted to computationally model the capillary bridge profiles and evaporation phenomenon with generic contact line dynamics (both CCR and CCA modes). The governing equations corresponding to the transport processes in both the liquid and gaseous domains are simulated in a fully coupled manner with appropriate boundary conditions to precisely trace the liquid-vapor interface and the three-phase contact point during evaporation. The effect of the bridge confinement phenomenon, i.e., the extent of confined ambient surrounding the liquid-vapor interface between the solid surfaces, is explored. Also, the role of wetting state and contact line dynamics during CCR and CCA modes of evaporation were probed, and good agreement with experimental observations was noted. Results show that the evaporation rate is primarily dictated by the confinement phenomenon, and wettability effects play a marginal role. A higher confinement curtails the evaporation rate due to an increased local vapor concentration around the liquid bridges. However, the wetting state substantially affects the internal Marangoni effect dynamics and the Stefan advection dynamics due to its explicit influence on the nonuniform evaporative flux along the liquid-vapor interface. Between superhydrophobic confinements, the contact lines are confined in the wedge-shaped region, thereby locally augmenting the vapor concentration. As a result, the large evaporative flux near the bulge region develops a higher temperature gradient, thereby inducing upscaled thermal Marangoni flow compared to hydrophilic confinements. These findings may have significant implications for the efficient designing and development of thermofluidic systems involving thermal transport, mixing, and deposition of dissolved particles in liquid bridges.

The Impact of Flapping Trajectories on the Induced Thrust of a Single and Tandem Configuration Flapping Foil

Abstract The development of propulsion devices by using the propulsive mechanisms of aquatic animals such as fish is a challenging task. An attempt has been made to replicate the fishtailed motion that caused thrust in the current investigation. At a low Reynolds number of Re = 1173, the propulsive performance of National Advisory Committee for Aeronautics 0012 flapping foils enduring distinct flapping trajectories (fishtailed and elliptical) is evaluated. A dynamic mesh arbitrary Lagrangian–Eulerian framework is used to understand the desired flapping motion of the foils while solving the flow via incompressible Navier–Stokes equations. Along with the flapping trajectory, the effects of the Strouhal number (St), inter-foils distance (Lx), and phase angle (φ) between the foils on the produced thrust are examined. The results demonstrate that using tandem configuration flapping foil with elliptical and fishtailed flapping can significantly increase the induced thrust and propulsive efficiency.

A hybrid multi-scale/finite element method in arbitrary Lagrangian-Eulerian framework for predicting nonlinear structural-acoustic responses of a large-deformable beam in fluid

This paper introduces a novel hybrid multi-scale/arbitrary Lagrangian-Eulerian finite element method (HMS/ALE-FEM) for addressing the nonlinear vibro-acoustic problem of a large-deformed beam in an infinite fluid. In the HMS/ALE-FEM, the vibrational response of the beam is tackled through modal superposition and a temporal multi-scale approach, while the acoustic wave emitted from the beam is addressed using the arbitrary Lagrangian-Eulerian finite element method (ALE-FEM). An alternating frequency/time domain technique is employed to handle the displacement and velocity of the moving mesh and the acoustic pressure on the beam surface. To validate the HMS/ALE-FEM, it is compared against the finite element method for beam response and the ALE-FEM for acoustic response, serving as a reference method. Taking the nonlinear vibro-acoustic problem of a buckled beam with 2:1 internal resonance as an example, the results of the HMS/ALE-FEM are compared with those of the reference method. The results show that the HMS/ALE-FEM is in good agreement with the reference method under different harmonic excitation amplitudes and frequencies. Due to the 2:1 internal resonance, double modes can be generated, and the second mode amplitudes of both beam displacement and acoustic pressure remain constant as the excitation amplitude varies. Notably, the HMS/ALE-FEM provides direct access to mode amplitude and phase information for beam displacement and acoustic pressure on the beam surface, offering valuable insights into fluid-structure interaction mechanisms in both single- and double-mode scenarios.

Nonlinear supersonic flutter of a composite panel backed by an acoustic cavity with finite-amplitude sound waves

In this paper, an implicit partitioned fluid-structure-acoustic interaction method is presented for predicting nonlinear aeroelastic response of an elastic composite laminated panel backed by an acoustic cavity and subject to a supersonic flow. The method is formulated in an arbitrary Lagrangian-Eulerian framework based on the unsteady Navier-Stokes equations for the supersonic flow, a geometrical nonlinear dynamics model for the composite laminated panel, and the nonlinear Westervelt equation for the finite-amplitude sound waves in cavity. A theoretical fluid-structure-acoustic model of the supersonic panel is proposed for validating the present numerical method, in which the nonlinear structural model of the panel, the first-order piston aerodynamics model of the supersonic flow and the nonlinear sound wave model of the cavity are coupled in a monolithic manner. It is found that cavity acoustic resonance can appear in the case a vibration mode of the panel coalescing with an acoustic mode of the cavity. Several new physical features of nonlinear acoustic resonance have been discovered, such as the presence of shock wave with high pressure gradients travelling along the resonant cavity in axial direction and the presence of higher-order harmonic wave components, which emphasize a nonlinear acoustic wave model of the cavity must be used to fully characterize these phenomena. In addition, the nonlinearity of the standing wave is quantitatively related to the acoustic modes by means of a proper orthogonal decomposition analysis.

A yarn-scale woven fabric model including significant slippage formulated within the Arbitrary Lagrangian Eulerian framework

A numerical model is proposed to simulate significant yarn slippage and unweaving in woven fabrics using the Arbitrary Lagrangian Eulerian (ALE) method. Woven fabrics were modeled at the yarn scale using 1D ALE elements with additional slip displacement degrees of freedom (DOF). The relatively weak bending stiffness of the yarn was included using a rotation-free approach. A weave kinematic constraint between crossing yarns allowed an efficient description of the deformation modes due to the yarn assembly such as in-plane shear. In particular, normal compaction at weave points was taken into account using an additional crimp amplitude DOF and couplings of the fabric’s cohesion with the normal and lateral compaction were considered. To deal with yarn unweaving, a specific void-ALE 1D element was developed in order to avoid remeshing, time-step reduction (explicit scheme) and early deactivation of the weave kinematic constraint. To demonstrate the capabilities of this numerical model, common characterization tests such as in-plane and out-of-plane pullouts, which induced unweaving were simulated. Finally, a first forming simulation on a hemisphere was performed to verify whether the cohesion of the fabric remained well represented in situations without loss of cohesion before simulating forming on a prismatic punch involving significant yarn slippage.

Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow

We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve. For the two-phase Navier-Stokes equations, we introduce both conservative and nonconservative ALE weak formulations in the 2d meridian half-plane. Piecewise linear parametric elements are employed for discretizing the moving interface, which is then coupled to a moving finite element approximation of the bulk equations. This leads to a variety of ALE methods, which enjoy either an equidistribution property or unconditional stability. Furthermore, we adapt these introduced methods with the help of suitable time-weighted discrete normals, so that the volume of the two phases is exactly preserved on the discrete level. Numerical results for rising bubbles and oscillating droplets are presented to show the efficiency and accuracy of these introduced methods.

Lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present life▪-cfd, an open-source CFD solver for cardiovascular simulations based on the life▪ finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and examples on how to use life▪-cfd. We verify the code through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The life▪-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments. Program summaryProgram Title:life▪-cfdCPC Library link to program files:https://doi.org/10.17632/hzsnc3jgds.1Developer's repository link:https://gitlab.com/lifex/lifex-cfdLicensing provisions:LGPLv3Programming language: C++ (standard ≥17)Supplementary material:https://doi.org/10.5281/zenodo.7852088 contains the application executable in binary form, compatible with any recent enough x86-64 Linux system, assuming that glibc version ≥ 2.28 is installed. Data and parameter files necessary to replicate the test cases described in this manuscript are also available.Nature of problem: The program allows to run computational fluid dynamics simulations of cardiovascular blood flows in physiological and pathological conditions, modeled through incompressible Navier-Stokes equations, including moving cardiac valves, moving domains (such as contracting cardiac chambers) in the arbitrary Lagrangian-Eulerian framework, and transition-to-turbulence flow. Given the scale of the typical applications, the program is designed for parallel execution.Solution method: The equations are discretized using the Finite Element method, on either tetrahedral or hexahedral meshes. The software builds on top of deal.II, implementing the mathematical models and numerical methods specific for CFD cardiovascular simulations. Parallel execution exploits the MPI paradigm. The software supports both Trilinos and PETSc as linear algebra backends.Additional comments including restrictions and unusual features: The program provides a general-purpose executable that can be used to run CFD simulations without having to access or modify the source code. The program allows to setup simulations through a user-friendly yet flexible interface, by means of readable and self-documenting parameter files. On top of that, more advanced users can modify the source code to implement more sophisticated test cases. life▪-cfd supports checkpointing, i.e. simulations can be stopped and restarted at a later time.

A conservative sharp interface method for two-dimensional incompressible two-phase flows with phase change

A conservative sharp interface method is proposed in this work to simulate two-dimensional/axisymmetric incompressible two-phase flows with phase change. In this method, we use the cut cell method to generate unstructured meshes near the interface, of which the cell edges overlap with the interface at each time step. On such mesh, the mass and heat transfer during phase change and all the jump conditions can be incorporated into the calculation of fluxes at the cell edges, to ensure that they are strictly satisfied at the interface in a sharp manner. The governing equations, including the incompressible Navier–Stokes equations, heat equation, and vapor mass fraction equation, are discretized by a second-order finite volume method in the arbitrary Lagrangian–Eulerian framework. To well couple the mass, heat, momentum, and interface evolution, the solution procedure is carefully designed and performed with several techniques. In such a way, the sharp discontinuity of the velocity, stress, temperature gradient, and vapor fraction, caused by the mass/heat transfer during phase change, can be simulated accurately and robustly. The performance of this method is systematically examined by cases of phase change at or below the saturated temperature, including vapor bubble in superheated liquid, film boiling, droplet evaporation at different relative humidity conditions, droplet evaporation under gravity, and droplet evaporation under forced convection. The applicability of the present method for incompressible two-phase flows with phase change is well demonstrated by comparing the numerical results with the benchmark, theoretical or experimental ones.

Transients of Marangoni and Stefan advection dynamics during generic sessile droplet evaporation

We probe the transient evolution of Marangoni thermo-hydrodynamics in the liquid domain and the Stefan advection in the gaseous domain during evaporation of sessile droplets with generic contact line dynamics [both constant contact radius (CCR) and constant contact angle (CCA) modes]. A transient arbitrary Lagrangian–Eulerian framework was considered to computationally model the evaporation phenomenon over the droplet lifetime. The governing equations corresponding to the transport processes in both liquid and gaseous domains are simulated in a fully coupled manner, while precisely tracing the liquid–vapor interface and three phase contact line. The effects of the wetting state and contact line dynamics during CCR and CCA modes were explored, and good agreement with experimental observations is noted. The results show that the non-uniformity in an internal temperature field due to evaporation leads to formation of multi-vortex Marangoni patterns in the flow field at initial periods. At the quasi-stable state, the temperature variation becomes monotonic, thereby resulting in a single recirculation vortex in both liquid and gaseous domains. For the CCR mode, the strength of these advection fields is solely governed by a critical contact angle of ∼32°, which is determined to correspond to the critical Marangoni number. Beyond this critical point, viscous action becomes significant, and the fluid motion mitigates progressively with the formation of twin vortices at final stages due to localized heat advection near the contact line. For the CCA mode, the strength of initial vortices augments with progressing time due to amplified evaporative fluxes at smaller contact radius. The internal thermofluidic patterns and evaporative modes in turn modulate the external Stefan flow fields and neighborhood temperature fields. These findings may hold strong implications for efficient functioning of practical droplet based processes involving transport, mixing, and deposition of dissolved particles.