Finite Volume Solver Research Articles

Fluid–structure interaction simulations of wind gusts impacting a hyperbolic paraboloid tensile structure

The paper focuses on fluid–structure interactions (FSI) between a turbulent, gusty fluid flow, and a membrane structure. Lightweight structures are particularly vulnerable to wind gusts and can be completely destroyed by them, making it essential to develop and evaluate numerical simulation methods suited for these types of problems. In this study, a thin-walled membrane in the shape of a hyperbolic paraboloid (hypar) is analyzed as a real-scale example. The membrane structure is subjected to discrete wind gusts of varying strength from two different directions. A partitioned FSI approach is employed, utilizing a finite-volume flow solver based on the large-eddy simulation technique and a finite-element solver developed for shell and membrane structures. A recently proposed source-term formulation enables the injection of discrete wind gusts within the fluid domain in front of the structure. In a step-by-step analysis, first the fluid flow around the structure, initially assumed to be rigid, is investigated, including a grid sensitivity analysis. This is followed by examining the two-way coupled FSI system, taking the flexibility of the membrane into account. Finally, the study aims to assess the impact of wind gusts on the resulting deformations and the induced stresses in the tensile material, with a particular focus on the influence of different wind directions.

Analysis of ansys fluent for Wall-Modeled Large-Eddy Simulation of Turbulent Channel Flow

Abstract This study assesses the accuracy of ansysfluent 19.2, a commonly employed general-purpose finite volume solver, in the context of wall-modeled large-eddy simulation for turbulent channel flow at a moderate Reynolds number, Reτ=2000. The sensitivity of the solution to variations in grid resolution, aspect ratio, grid arrangement (collocated versus staggered), and subgrid-scale (SGS) model is analyzed and contrasted to results from a corresponding direct numerical simulation (DNS) and a mixed pseudospectral and finite differences solver. Results indicate good convergence of first- and second-order statistics from the staggered grid setups as the grid is refined, whereas no clear trend is observed in cases with collocated grid setups. Velocity spectra show a lack of an apparent inertial range trend and rapid decay of energy density at high wavenumbers, with a spurious energy pile-up near the cutoff wavenumber indicating the presence of unphysical oscillations in the velocity fields. Grid refinement strengthens such oscillations in collocated grid setups and reduces them in staggered grid setups. Two-point streamwise velocity autocorrelation maps reveal an underprediction of turbulent structure size. In contrast, cross-stream autocorrelations agree with corresponding curves from direct numerical simulation, showing signatures of alternating high- and low-momentum streaks in the logarithmic layer.

A novel framework of the lattice Boltzmann model for multilayer shallow water systems

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.

Aggregating nanoparticle transport with nonlinear attachment: Modeling and experimental validation

A conceptual mathematical model was developed to simulate the transport of migrating nanoparticles in homogeneous, water saturated, 1-dimensional porous media. The model assumes that nanoparticles can collide with each other and aggregate. Nanoparticles can be found attached reversibly and/or irreversibly onto the solid matrix of the aquifer or suspended in aqueous phase. Attached particles may either contribute to the acceleration of subsequent particle deposition or hinder it, leading to the ripening or blocking process, respectively. The aggregation process was simulated based on the Smoluchowski Population Balance Equation (PBE) and was coupled with the advection-dispersion-attachment equation (ADA) to form a family of partial differential equations that govern the migration of nanoparticles in porous media. For the solution of the PBE, an efficient finite volume solver was employed that significantly accelerated computation times, by reducing the number of participating equations, while maintaining the required accuracy. The developed model was applied to nanoparticle transport experimental data available in literature. The model successfully matched the breakthrough concentration curves, and estimated the corresponding nanoparticle diameter, proving its ability to capture the physical processes participating in nanoparticle transport.

GPU accelerated Staggered Update Procedure (SUP)

The advancement in programmable capability of graphics hardware has paved new opportunities in the domain of high performance computing (HPC). The computational fluid dynamics (CFD) community, being a significant user of HPC, has started exploiting the inherent data parallelism in the numerical solvers to be able to make efficient use of these many-core, high throughput accelerator based processors. In the present work, we examine the process of accelerating our CPU based Staggered Update Procedure (SUP) solver, i.e., a higher order accurate cell-centred finite volume solver by off-loading the computationally most expensive region of the code pertaining to the explicit residual computation. We have adopted OpenACC, a directive based programming model to expose parallelism in the code. The framework evolved for GPU porting in the context of SUP is also of value to those intending to port their CFD solvers based on classical finite volume methodology. The performance analysis is conducted using scalar convection–diffusion equations in both two- and three-dimensions. The findings demonstrate a speedup factor of 9 (in case of 2D) and 28 (in case of 3D) when considering the explicit residual alone, achieved with a single NVIDIA Tesla V100 GPU card. In addition, we could establish superior algorithmic scalability by the way of recovering near perfect serial performance, on the heterogeneous CPU+GPU architecture. Further, overall code acceleration can be achieved by porting other parts of the solver on GPU.

Impact of energy deposition as active flow control on scramjet inlet performance using Immersed Boundary Method

This study investigates the impact of upstream energy deposition as an active flow control method on the performance of a two-dimensional scramjet inlet through numerical simulations. An in-house inviscid finite volume solver was employed for the simulations, with boundary reconstruction of the scramjet achieved using a ghost-cell based immersed boundary method. The effects of different energy spot locations, various energy strengths, and different freestream Mach numbers on the scramjet performance were thoroughly analyzed. Four inlet parameters, namely, mass capture ratio (μ), total pressure ratio (TPR), kinetic energy efficiency (ηKE), and flow distortion index (DI), were used to assess the scramjet performance. The analysis revealed that energy deposition significantly reduced flow distortion, resulting in noticeable improvements in mass flux and total pressure ratio. However, kinetic energy efficiency exhibited minimal change. The study provides comprehensive insights into the impact of energy deposition on scramjet performance, highlighting its potential for enhancing inlet characteristics.

GPU-Enabled Exascale Quantum Transport Modeling of Carbon Nanotube Devices

The work will describe our efforts to develop an exascale electrostatic-quantum transport framework, Quantum-eXstatic (https://github.com/AMReX-Microelectronics/eXstatic), currently supporting the modeling of carbon nanotube field-effect transistors (CNTFETs). The framework is capable of modeling realistic three-dimensional structures, efficiently, using CPU/GPU heterogeneous architectures of state-of-the-art supercomputers. It is built on top of the AMReX library, which is a GPU-enabled software library containing functionality for writing particle-mesh applications on structured grids. The Quantum-eXstatic framework comprises three major components: the electrostatic module, the quantum transport module, and the part that self-consistently couples the two modules. The electrostatic module using a finite-volume multigrid solver to compute the electrostatic potential induced by charges on the surface of carbon nanotubes, as well as by source, drain, and gate terminals, which can be modeled using an embedded boundary approach to allow for intricate shapes. The quantum transport module uses the Nonequilibrium Green's Function (NEGF) method to model induced charge. Currently, it supports coherent (ballistic) transport, mode-space approximation for subbands of nanotube, contacts modeled as semi-infinite leads, and Hamiltonian representation using the tight-binding approximation. Special features are being included for accurate modeling of long nanotubes, such as adaptive refinement of integration contours to resolve van Hove singularities in long channels. Particular attention is paid to overlap computations with communication to optimize GPU performance. The self-consistency between the two modules is achieved using Broyden's modified second algorithm, which is parallelized using CPUs and GPUs. Preliminary scaling studies show that the code exhibits ~77% weak-scaling efficiency on 512 NVIDIA A100 GPUs of Perlmutter supercomputer for modeling gate-all-around CNTFETs with a channel length of 13.5 microns at equilibrium conditions. This case involved computations of electrostatic potential in 14.5 billion computational cells and Green’s function computation for a Hamiltonian of size 131,072 x 131,072. For problems of this large size, the code takes about 5 min to reach self-consistency. Figure 1

A well-balanced finite volume solver for the 2D shallow water magnetohydrodynamic equations with topography

In this paper, a second-order finite volume Non-Homogeneous Riemann Solver is used to obtain an approximate solution for the two-dimensional shallow water magnetohydrodynamic (SWMHD) equations considering non-flat bottom topography. We investigate the stability of a perturbed steady state, as well as the stability of energy in these equations after a perturbation of a steady state using a dispersive analysis. To address the elliptic constraint ∇⋅hB=0, the GLM (Generalized Lagrange Multiplier) method designed specifically for finite volume schemes, is used. The proposed solver is implemented on unstructured meshes and verifies the exact conservation property. Several numerical results are presented to validate the high accuracy of our schemes, the well-balanced, and the ability to resolve smooth and discontinuous solutions. The developed finite volume Non-Homogeneous Riemann Solver and the GLM method offer a reliable approach for solving the SWMHD equations, preserving numerical and physical equilibrium, and ensuring stability in the presence of perturbations.

Implementation of a high-order spatial discretization into a finite volume solver: Applications to turbomachinery test cases using an eddy-viscosity turbulence closure

In this study, the implementation of a high-order spatial discretization method into a Finite Volume solver is presented. Specific emphasis is put on the analysis of the performance over selected turbomachinery test cases. High-order numerical discretization is achieved by adopting the cell-centered Least-Square reconstruction, which is implemented in the in-house solver HybFlow. The validation of the adopted methodology is performed by assessing the solution of a turbulent flat plate with zero pressure gradient, using a eddy-viscosity transitional model. The test case also evidences the effect of the discretization of gradient-based source terms when a high-order reconstruction methodology is used. In the second part of the paper, the solver is used for the solution of relevant two-dimensional turbomachinery test cases, assessing the impact of 2nd and 3rd order reconstruction on the prediction of the aerodynamics and the heat transfer for respectively a low-pressure blade and a high-pressure turbine vane. It is shown how a high-order reconstruction allows for obtaining a better prediction of turbomachinery aerodynamics, with lower number of elements. The benefits over heat transfer predictions in high Reynolds number conditions are instead limited to the reduction of heat transfer coefficient spikes in under-resolved regions of the blade. Eventually, the methodology is validated for a three-dimensional low-pressure turbine cascade with realistic boundary layer inflow conditions.

A robust and well-balanced finite volume solver for investigating the effects of tides on water renewal timescale in the Nador lagoon, Morocco

Coastal lagoons, particularly those not well-connected to the sea, are highly susceptible to continuous water retention, adversely affecting water quality and ecosystems. Understanding and quantifying the processes governing water renewal in such semi-enclosed regions is crucial. Using the principles of constituent-oriented age and residence time theory (www.climate.be/cart), we calculated timescales to explain the water renewal process in semi-enclosed areas. To improve our understanding and define the dynamics of the Nador lagoon, we use two distinct time scales: residence time and exposure time. Residence time indicates the length of time a parcel of water leaves the region of interest for the first time, while exposure time represents the overall length of time a parcel of water remains in that region, including any subsequent inflows. The modeling system adopts an Eulerian approach, including two interlinked model components: the shallow-water equations incorporating bottom friction, eddy viscosity, wind shear stresses, momentum diffusion, and Coriolis forces for modeling hydrodynamics, and a transport-diffusion equation utilized to simulate the advection and diffusion of the passive tracer concentration. The entire system is integrated into a high-order finite volume solver that employs unstructured meshes, upwind numerical fluxes, and slope limiters to achieve precise resolution of steep bathymetric gradients that may arise in the approximate solution. The scheme is non-oscillatory and preserves the conservation properties. In this research, we explore various situations related to the connection between the Mediterranean Sea and the Nador lagoon. Specifically, we suggest novel entry points that have the potential to significantly decrease the water residence within the lagoon.

A face-centred finite volume method for laminar and turbulent incompressible flows

This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the negative Spalart–Allmaras (SA) model and three novel convective stabilisations, inspired by Riemann solvers, are derived and compared numerically. The resulting method achieves first-order convergence of the velocity, the velocity-gradient tensor and the pressure. FCFV accurately predicts engineering quantities of interest, such as drag and lift, on unstructured meshes and, by avoiding gradient reconstruction, the method is less sensitive to mesh quality than other FV methods, even in the presence of highly distorted and stretched cells. A monolithic and a staggered solution strategies for the RANS-SA system are derived and compared numerically. Numerical benchmarks, involving laminar and turbulent, steady and transient cases are used to assess the performance, accuracy and robustness of the proposed FCFV method.

A Liouville optimal control framework in prostate cancer

In this work we present a new stochastic framework for obtaining optimal treatment regimes in prostate cancer. We model the realistic scenario of randomized clinical trials for incorporating randomness related to interaction between a prostate cancer cell and androgen cell quota, due to cancer heterogeneities, across different patients in a given group, using a Liouville partial differential equation. We then solve two optimization problems: one for determining the model parameters to fit the measured data and the second to determine the optimal androgen deprivation therapy. The optimization problems are implemented using a positive, stable, and conservative finite volume solver for the Liouville equations and the projected non-linear conjugate gradient method. Several numerical results, including comparison with ordinary differential equations modeling framework, demonstrate the robustness and accuracy of our proposed framework to obtain optimal treatment regimes in real time.

Implementation of a GPU-enhanced multiclass soil erosion model based on the 2D shallow water equations in the software Iber

We present the implementation of a new fully distributed multiclass soil erosion module. The model is based on a 2D finite volume solver (Iber+) for the 2D shallow water equations that computes the overland flow water depths and velocities. From these, the model evaluates the transport of sediment particles due to bed load and suspended load, including rainfall-driven and runoff-driven erosion processes, and using well-established physically-based formulations. The evolution of the mass of sediment particles in the soil layer is computed from a mass conservation equation for each sediment class. The solver is implemented using High Performance Computing techniques that take advantage of the computational capabilities of standard Graphical Processing Units, achieving speed-ups of two orders of magnitude relative to a sequential implementation on the CPU. We show the application and validation of the model at different spatial scales, ranging from laboratory experiments to meso-scale catchments.

Flow past triangular airfoil of variable thickness with low Reynolds number in Mars atmosphere

Aerodynamic research on Mars for the past few decades has increased in the development of optimum aerial vehicles for Mars. The current research aims to study the aerodynamics of a triangular airfoil in Mars atmospheric conditions and understand the future regions of flow improvement. A numerical investigation using a Finite Volume Solver has been performed for 0° to 16° angles of attack at low and high flow velocities. Low flow velocities ranging from Re = 3,000 to 7,000 have been considered for the investigation. The nonlinearity in Cl appears as the separation bubble begins to approach the apex on the suction surface. Apart from the separation bubble, a flow recirculation zone is generated for low and high Re. at α = 16°. The highest aerodynamic performance is at α = 6°.

A hybrid CPU‐GPU paradigm to accelerate reactive CFD simulations

AbstractThe solution of reactive computational fluid dynamics (CFD) simulations is accelerated by the implementation of a hybrid central processing unit/graphics processing units (CPU/GPU) Finite Volume solver based on the operator‐splitting strategy, where the chemistry integration is treated independently of the flow solution. The integration of ordinary differential equations (ODEs) describing the finite‐rate chemical kinetics is solved by an adaptive multi‐block explicit solver on GPUs, while the load of the fluid solution is distributed on a multicore CPU algorithm. The resulting speed‐up for reactive CFD simulations is up to 10; the performance gain increases with the size of the mechanism. The proposed implementation is general and can be applied to any CFD problem where the governing equations for the fluid transport are coupled with an ODE system. Code validation is performed against reference solutions on a selection of test cases involving reacting flows.

Combination of Advanced Actuator Line/Disk Model and High-Order Unstructured Finite Volume Solver for Helicopter Rotors

In the research field of rotorcraft aerodynamics, there are two fundamental challenges: resolving the complex vortex structures in rotor wakes and representing the moving rotor blades in the ambient airflow. In this paper, we address the first challenge by utilizing a third-order unstructured finite volume solver, which exhibits lower numerical dissipation than its second-order counterpart. This allows for sufficient resolution of small vortex structures on relatively coarse meshes. With this flow solver, the second challenge is addressed by modeling each rotor as an actuator disk (i.e., the actuator disk model (ADM)) or modeling each blade as an actuator line (i.e., the actuator line model (ALM)). Both of the two models are equipped with an improved tip loss correction, which is introduced in detail in the methodology section. In the section of numerical experiments, the numerical convergence properties of the two types of solvers have been compared in the case of two-dimensional infinite wing. In addition, the relationship between the ALM and the lifting line theory is discussed in the cases of fixed-wing calculations. Another goal of these cases is to validate the tip loss correction presented. The validation of the ALM/ADM and comparisons of computational efficiency are also demonstrated in simulations involving both hover and forward flight rotors. It was found that the combination of the third-order finite volume solver and the ALM/ADM with the improved tip loss correction presents an efficient way of performing the aerodynamic analysis of rotor-induced downwash flow.

Surface Reaction of Electroosmotic Flow-Driven Free Antigens With Immobilized Magnetic-Microbeads-Tagged-Antibodies in Microchannels.

Immunoassays based on reactions between target pathogen (antigen; Ag) and antibody (Ab) are frequently used for Ag detection. An external magnetic field was used to immobilize magnetic microbeads-tagged-antibodies (mMB-Ab) on the surface of a microchannel in the capture zone. The mMB-Ab was subsequently used for Ag detection. The objective of this numerical study, with experimental validation, is to assess the surface reaction between mMB-Ab and Ag in the presence of electro-osmotic flow (EOF). First, immobilization of mMB-Ab complex in the wall of the capture zone was achieved. Subsequently, the Ag was transported by EOF toward the capture zone to bind with the immobilized mMB-Ab. Lastly, mMB-Ab:Ag complex was formed and immobilized in the capture zone. A finite volume solver was used to implement the above steps. The surface reaction between the mMB-Ab and Ag was investigated in the presence of electric fields (E): 150 V/cm-450 V/cm and Ag concentrations: 0.001 M-1000 M. The depletion of mMB-Ab increases with time as the E decreases. Furthermore, as the concentration of Ag decreases, the depletion of mMB-Ab increases with time. These results quantify the detection of Ag using the EOF device; thus, signifying its potential for rapid throughput screening of Ag. This platform technology can lead to the development of portable devices for the detection of target cells, pathogens, and biomolecules for testing water systems, biological fluids, and biochemicals.

Scramjet Intake Aerodynamic Studies Using Sharp Interface Immersed Boundary Method

In this present article, the use of a throttling device in the form of movable flap to study scramjet inlet unstart has been investigated numerically. The flap has been employed as an effort to simulate the rise in combustor pressure of the scramjet. Computational analysis for freestream Mach number and freestream pressure of and respectively, have been performed by a two-dimensional compressible CFD in-house Finite volume solver for perfect gas. Convective fluxes have been evaluated using AUSM scheme.Inviscidflow has been assumed for all the simulations. Particular point of interest in these simulations is the application of Immersed Boundary Method along the wall boundaries,enabling the use of structured grid for complex geometries. The results demarcate the starting condition of the inlet based on the flap throttling values. Comparative results in the form of Mach number and pressure contours are presented for different flap positions. The use of Immersed Boundary Method has been successfully displayed bysimulating a movable flap.

Investigation of numerical phase transition of nano-enhanced SiC/paraffin wax PCM in solar-assisted water desalination system

Adding nanoparticles in phase change material (PCM) is a new trend for enhancing their thermal energy-storing ability as well as thermal conductivity. From this point of view, a numerical study is carried out to examine the addition of silicon carbide nanoparticles in paraffin wax PCM, used as heat energy storing material in a semi-cylindrical solar water desalination system. The PCM temperature is maintained at 52 °C and the semi-cylindrical tubular section has a wall temperature of 85 °C. The top plane section of the tubular solar collector is made up of graphite material. A semi-circular cross-section is selected for numerical analysis. A finite volume solver is used for solving thermal and fluid flow governing equations. A pressure staggering option algorithm is applied for pressure–velocity coupling. The temporal parameters like temperature, velocity contours, melting fraction, enthalpy, and entropy of nano silicon embedded paraffin wax PCM are widely discussed. The results clearly show that the phase transition of solid PCM to fluid PCM is greatly influenced by nanoparticle addition and enhances the rate of heat transfer. Initially for the first 60 min the melting fraction and temperature of PCM remain uniform as the time step increases above 60 min the behavior of PCM changes abruptly which clearly indicates the random distribution of nanoparticles within the PCM. A critical time and temperature limit exists for nanoparticles-based PCM beyond which, the thermal efficiency of the solar water desalination system gets influenced.

Introducing cuDisc: a 2D code for protoplanetary disc structure and evolution calculations

ABSTRACT We present a new two-dimensional (2D) axisymmetric code, cuDisc, for studying protoplanetary discs, focusing on the self-consistent calculation of dust dynamics, grain-size distribution and disc temperature. Self-consistently studying these physical processes is essential for many disc problems, such as structure formation and dust removal, given that the processes heavily depend on one another. To follow the evolution over substantial fractions of the disc lifetime, cuDisc uses the cuda language and libraries to speed up the code through GPU acceleration. cuDisc employs a second-order finite-volume Godonuv solver for dust dynamics, solves the Smoluchowski equation for dust growth, and calculates radiative transfer using a multifrequency hybrid ray-tracing/flux-limited-diffusion method. We benchmark our code against current state-of-the-art codes. Through studying steady-state problems, we find that including 2D structure reveals that when collisions are important, the dust vertical structure appears to reach a diffusion-settling-coagulation equilibrium that can differ substantially from standard models that ignore coagulation. For low fragmentation velocities, we find an enhancement of intermediate-sized dust grains at heights of ∼1 gas scale height due to the variation in collision rates with height, and for large fragmentation velocities, we find an enhancement of small grains around the disc mid-plane due to collisional ‘sweeping’ of small grains by large grains. These results could be important for the analysis of disc spectral energy distributions or scattered light images, given these observables are sensitive to the vertical grain distribution.