Geometry Of Computational Domain Research Articles

Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner. The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.

Isogeometric Analysis Approximation of Linear Elliptic Equations with L1 Data

Isogeometric Analysis (IgA) is a recent technique for the discretization of Partial Differential Equations (PDEs). The main feature of the method is the ability to maintain the same exact description of the computational domain geometry throughout the analysis process, including refinement. In the present paper, we consider, in dimension d >= 2 the Isogeometric Analysis approximation of second order elliptic equations in divergence form with right-hand side in L1 . We assume that the family of meshes is shape regular and satisfies the discrete maximum principle. When the right-hand side belongs to L1(\Omega), we prove that the unique solution of the discrete problem converges to the unique renormalized solution in W01,q(\Omega), 1 <= q < d/(d-1) . We also prove some error estimates and include numerical tests for data with low smoothness.

Adjustment of a Mathematical Model of Gas Fuel Combustion Taking into Account Computational Domain Geometry Refinement

Adjustment of a Mathematical Model of Gas Fuel Combustion Taking into Account Computational Domain Geometry Refinement

XIGA: An eXtended IsoGeometric analysis approach for multi-material problems

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining accurate solutions remain challenging. Immersed boundary techniques provide elegant solutions for such problems. Enrichment methods alleviate the need for generating conforming analysis grids by capturing discontinuities within mesh elements. Additionally, increased accuracy of physical responses and geometry description can be achieved with higher-order approximation bases. In particular, using B-splines has become popular with the development of IsoGeometric Analysis. In this work, an eXtended IsoGeometric Analysis (XIGA) approach is proposed for multi-material problems. The computational domain geometry is described implicitly by level set functions. A novel generalized Heaviside enrichment strategy is employed to accommodate an arbitrary number of materials without artificially stiffening the physical response. Higher-order B-spline functions are used for both geometry representation and analysis. Boundary and interface conditions are enforced weakly via Nitsche’s method, and a new face-oriented ghost stabilization methodology is used to mitigate numerical instabilities arising from small material integration subdomains. Two- and three-dimensional heat transfer and elasticity problems are solved to validate the approach. Numerical studies provide insight into the ability to handle multiple materials considering sharp-edged and curved interfaces, as well as the impact of higher-order bases and stabilization on the solution accuracy and conditioning.

Потенціал в області мікронерівностей поверхні металу, який працює в режимі катодного захисту

This effort presents the results of investigation of cathodic protection process of a section of the main pipeline, which has been operating in cathodic protection mode for a long time and which insulation has completely exfoliated from metal surface, and a cavity between is filled with water and salt impurities. In this case, a decisive factor is a fact that a metal surface is covered with microroughnesses in the form of protrusions with almost conical shape. The surface is immersed in electrolyte. At the electrolyte-metal interface, a potential difference is formed - a corrosion potential, which creates an unstable equilibrium among the potentials of metal and electrolyte. A mathematical model is designed and implemented into a numerical algorithm and computer program. A computational experiment has been carried out to calculate the potential around microroughness. The model describes a change in potential in this area at incomplete and complete cathodic protection of metal surface. The basis of computational model is a selection of one of metal protrusions of material microheterogeneity and placing it in a cylinder, which diameter coincides with that one of the lower base of this protrusion, and its upper part passes through the apex of the protrusion. Mathematical model equations with corresponding boundary conditions and their discrete implementation are presented. The solution of problems is obtained by iterative procedures based on reference values of protective potential taken from practice. The results of computational experiment are presented in the form of graphs: 1) potential distribution in the field of electrolytes; 2) changes in electrolyte potential at the border with protrusion at different values of polarization potential; 3) changes in polarization resistance in the area (calculated). The geometry of computational domain was also varied, and the values of protective potential were determined to ensure the absence of corrosion. Keywords: corrosion, microroughness, protective potential, plastic current density, electrolyte

Setting up the mathematical model of gas fuel combustion taking into account computational domain geometry refinement

The problem of gaseous fuel combustion in a land-used gas turbine engine combustion chamber was formulated, and the results of the numerical solution were described. The paper assumes that the gas-air mixture is a single-phase, multicomponent and reactive flow. The Reynolds averaging approach to the Navier-Stokes equations was used to describe the turbulent flow in the combustion chamber. The SST model of turbulence was used to close the averaged system .A combined EDM/FRC combustion model was used to determine the rate of formation of mixture components. A technique was proposed for setting up the mathematical model taking into account three parameters: the turbulent Prandtl and Schmidt numbers and the coefficient limiting the burning rate. Based on a comparison of the results of preliminary calculations and experiments, it was suggested that the difference in these data is due to technological deviations and the application of a heat-protective coating to the walls of the flame tube. The geometry of the computational domain was changed based on the airflow coefficient obtained in the aerodynamic tests. The setting up of the mathematical model was carried out both on the initial and on the refined geometry. The verification of the mathematical model was carried out using the results of experiments on three structural variants of the flame tube. The results of calculations carried out with the use of refined data showed that a change in geometry made it possible to more correctly describe combustion in a turbulent flow: the theoretical results on the average non-uniformity obtained on the refined geometry of the studied region practically coincide with the experimental data. Due to updating the geometry of the computational domain, it was possible to establish the location and magnitude of the maximum non-uniformity. Using the results obtained in this work, a mathematical model was developed to describe the combustion of gaseous fuel in the combustion chamber of a gas turbine engine. The proposed model can be used to further optimize the design of the combustion chamber.

On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem

In this paper a fluid-structure interaction problem for incompressible Newtonian fluids is studied. We prove the convergence of an iterative process with respect to the computational domain geometry moving according to a viscoelastic deformation. In our previous joint works on numerical approximation of similar problems we refer to this approach as the global iterative method [1,2]. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point Theorem, where the contractivity of the corresponding mapping is shown using the continuous dependence of the weak solution on the given domain deformation. This estimate is obtained by remapping the problem onto a fixed domain and using appropriate divergence-free test functions involving the difference of two solutions.

Numerical study on wave phenomena produced by the super high-speed evacuated tube maglev train

With the increasing demand of faster, safer, and more comfortable rail travel, the evacuated tube maglev train (ETMT) has gradually attracted hot concerns in recent years. According to Kantrowitz limit theory, ETMT may encounter chocked flows, leading to more complex generation and development of a series of waves as ETMT moves rapidly in the tube. To study the wave phenomena produced by ETMT running at the super high-speed, the computational domain geometry model was simplified and then 2-D axisymmetric compressible N-S equation was established in the paper. Dynamic mesh method and dynamic adaptive mesh method were used to simulate the real motion of ETMT and improve the capture accuracy of the waves respectively. Results show that the wave structure is mainly composed of expansion waves, reflected shock waves and normal shock waves as ETMT moves for enough time at the speed of 1250 km/h. The intensity of the normal shock wave in front of the head car experiences four states consisting of rapid increase, initial stability, sudden drop and final stability. In the wake, the flow velocity attenuates in a fluctuating way along the opposite motion direction of ETMT due to the complicated interaction between shock waves and expansion waves.

Three-dimensional numerical simulation of electromagnetic diffusion problem and magnetization effects

We present a newly developed algorithm for three-dimensional (3D) magnetotelluric model based on the vector finite element method. In this paper, unstructured grids which are composed of irregular tetrahedrons are used in our finite element model, which can be refined locally and adaptively according to the complex geometry of computational domain or subsurface structure. For obtaining more accurate solutions, secondary field rather than total field is numerically computed, which makes the errors limited to relatively small secondary field. Traditional node-based finite element method does not satisfy the condition that the normal electrical field is discontinuous at the interface of electric separatrix and the electrical current density is divergence-free throughout the regions without source, which obviously violates Maxwell equations. In order to overcome these drawbacks of node-based finite element, vector finite element method is employed to solve the secondary field-based partial differential equation. Moreover, in this study, the heterogeneous permeability is taken into consideration in our algorithm, as a consequence, which can deal with heterogeneous permeability model. The accuracy of our approach is verified by comparing with previously published numerical simulations of a COMMEMI-3D model. The advantages of our approach are also illustrated by the numerical simulations of model with arbitrary topography and complicated anomalous body. In addition, the simulation results of the irregular anomaly and the complex model of arbitrary terrain are both ideal results. It proves that the effect of 3D terrain is more serious and complex than that of two-dimensional (2D) terrain, and dealing with 3D models or data with 2D algorithm may bring in large errors. In the area where the magnetic permeability is abnormal, the magnetic permeability has an important influence on the numerical simulation results, and the magnetic permeability must be treated as an independent parameter in the magnetotellurics survey.

Rheology effect determination of the heterogeneous rock massif on the stress-strain state of the breakage face geomechanical system

The purpose of this study is to determine the nature of influence of the rheological properties of the rocks on the results of computational experiments simulating the mine workings contour condition during the breakage face advance. To determine the deformations along the mine workings contour, the calculations have been made of the junction area between the preparatory and stope face mine workings by the finite element method for various parameters of the material models. These data provided the basis for analysis of the patterns development of the rheology modelling influence on the stress-strain state of the geomechanical system. The obtained patterns are described by a function of many variables, and this function determines the limit and degree of rheology effect on the results of calculations. For the first time this pattern takes into account the heterogeneity of the rheological characteristics of rocks and the specifics of the computational domain geometry. The use of the obtained patterns makes it possible to simplify significantly the process of modelling in time and space of the geomechanical systems, which have a complex structure describing the interaction of several objects.

Three-dimensional flow with elevated helicity in driven cavity by parallel walls moving in perpendicular directions

The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow, yet having simple single-block cubical geometry of computational domain. The elevated level of helicity is caused by motion of a wall in the direction of axis of primary vortex created by a parallel wall. The velocity vector field is obtained numerically by using second-order upwind scheme and 2003 grid. Helicity, magnitude of normalized helicity, and kinematic vorticity number are evaluated for Reynolds numbers ranging from 100 to 1000. Formation of two primary vortices with their axis oriented perpendicularly and patterns of secondary vortices are discussed. Computational results are compared to the well-known 3-D recirculating cavity flow case where the lid moves in the direction parallel to the cavity side walls. Also results are compared to the diagonally top-driven cavity and to the cavity flow driven by moving top and side walls. The streamlines for the proposed flow show that the particles emerging from top and bottom of the cavity do mix well. Quantitative evaluation of mixing of two fluids in the proposed cavity flow confirms that mixing occurs faster than in the benchmark case.

Numerical prediction of thermo-aeraulic behavior for a cavity with internal linear heat source

Computational Fluid Dynamics (CFD) is a promising way, nowadays, to predict the air Flow in enclosures. As a result, the objective of this study is to assess the potential of CFD technique to predict the air Flows driven by buoyancy in heated real-scale rooms. The numerical model is validated using experimental data for fullscale test rooms; therefore, the experimental set-up is rst presented. This is followed by the numerical model description, focusing on its principal elements: computational domain geometry, discretization, turbulence model, radiation model, and thermal boundary conditions. In addition, a simpli ed approach is proposed to integrate a heat source in CFD models: Term source homogeneously spread all over the volume of the heat source. Comprehensive experimental-numerical comparisons are presented in terms of heat transfer to the walls of the test room, heat source behavior, and plume development. The results show that the model developed in this study leads to realistic predictions. Finally, the simpli ed CFD description of heat sources developed here can be extrapolated for other con gurations - di erent power, heat emission (convection/radiation), dimensions, and shape. Consequently, this method can be applied in detailed studies dealing with thermal comfort, indoor air quality, and energy consumption for heated rooms.

A coupled discrete element‐finite difference approach for modeling mechanical response of fluid‐saturated porous materials

SummaryA model of fluid‐saturated poroelastic medium was developed based on a combination of the discrete element method and grid method. The developed model adequately accounts for the deformation, fracture, and multiscale internal structure of a porous solid skeleton. The multiscale porous structure is taken into account implicitly by assigning the porosity and permeability values for the enclosing skeleton, which determine the rate of filtration of a fluid. Macroscopic pores and voids are taken into account explicitly by specifying the computational domain geometry. The relationship between the stress–strain state of the solid skeleton and pore fluid pressure is described in the approximations of simply deformable discrete element and Biot's model of poroelasticity. The developed model was applied to study the mechanical response of fluid‐saturated samples of brittle material. Based on simulation results, we constructed a generalized logistic dependence of uniaxial compressive strength on loading rate, mechanical properties of fluid and enclosing skeleton, and on sample dimensions. The logistic form of the generalized dependence of strength of fluid‐saturated elastic–brittle porous materials is due to the competition of two interrelated processes, such as pore fluid pressure increase under solid skeleton compression and fluid outflow from the enclosing skeleton to the environment. Copyright © 2015 John Wiley & Sons, Ltd.

Innovative and efficient stent flexibility simulations based on isogeometric analysis

Abstract One of the main properties of cardiovascular stents is to properly bend in order to accommodate the tortuous vascular structure and Finite Element Analyses (FEA) are currently the preferred computational tool to properly evaluate the stent response under bending. Isogeometric Analysis (IgA) has recently emerged as a cost-effective alternative to classical FEA, based on the use of typical CAD basis functions for both geometric description and variable approximation. This implies the capability to describe accurately the computational domain geometry and, typically, a better approximation of the solution with many fewer degrees of freedom with respect to FEA. Accordingly, this work aims at describing a computational framework based on IgA to evaluate the mechanical performance of endovascular stents. In particular, stent bending analyses involving large deformations are performed using both IgA and classical FEA for two carotid artery stent designs. The results discussed here suggest that for a given level of accuracy IgA attains a better performance with at least one order of magnitude fewer degrees of freedom than classical FEA. Moreover IgA shows an improved capability to reproduce local geometrical instabilities due to buckling.

A three-node triangular element with continuous nodal stress

A three-node triangular element with continuous nodal stress (Trig3-CNS) is presented. The present work is the development of the partition-of-unity based ‘FE-Meshless’ quadrilateral element with continuous nodal stress (Quad4-CNS). This triangular element, Trig3-CNS, is potential to replace Quad4-CNS when the geometry of computational domain is too complex to generate quadrilateral meshes. The three-node triangular element (Trig3) is widely used, however it is always of low accuracy due to its low order of trial functions. By increasing the order of trial functions, Trig3-CNS obtains better accuracy and higher convergence rate as compared to Trig3. The numerical tests in this paper demonstrate that Trig3-CNS has higher tolerance to mesh distortion as compared to the Trig3 and four-node quadrilateral element (Quad4). Another advantage is that the derivative of Trig3-CNS shape function is continuous at nodes, therefore Trig3-CNS is capable of giving smoother solution and calculating nodal stress without any extra smoothing operation.

RANS and Large Eddy Simulation of Internal Combustion Engine Flows—A Comparative Study

A comparative cold flow analysis between Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) cycle-averaged velocity and turbulence predictions is carried out for a single cylinder engine with a transparent combustion chamber (TCC) under motored conditions using high-speed particle image velocimetry (PIV) measurements as the reference data. Simulations are done using a commercial computationally fluid dynamics (CFD) code CONVERGE with the implementation of standard k-ε and RNG k-ε turbulent models for RANS and a one-equation eddy viscosity model for LES. The following aspects are analyzed in this study: The effects of computational domain geometry (with or without intake and exhaust plenums) on mean flow and turbulence predictions for both LES and RANS simulations. And comparison of LES versus RANS simulations in terms of their capability to predict mean flow and turbulence. Both RANS and LES full and partial geometry simulations are able to capture the overall mean flow trends qualitatively; but the intake jet structure, velocity magnitudes, turbulence magnitudes, and its distribution are more accurately predicted by LES full geometry simulations. The guideline therefore for CFD engineers is that RANS partial geometry simulations (computationally least expensive) with a RNG k-ε turbulent model and one cycle or more are good enough for capturing overall qualitative flow trends for the engineering applications. However, if one is interested in getting reasonably accurate estimates of velocity magnitudes, flow structures, turbulence magnitudes, and its distribution, they must resort to LES simulations. Furthermore, to get the most accurate turbulence distributions, one must consider running LES full geometry simulations.

CFD modeling of buoyancy driven cavities with internal heat source—Application to heated rooms

The aim of this work is to examine the capacity and the accuracy of a CFD (Computational Fluid Dynamics) model to characterize the thermo-aeraulic behavior of a heated room. Firstly, we present a brief description of the experimental set-up taken into account (two experimental tests with changed room boundary conditions were taken into account). Afterwards, the focus is on the main features of the numerical model (that strongly influence the accuracy of results): computational domain geometry and discretization, turbulence model, near wall treatment, radiation model and thermal boundary conditions. In addition, a simplified approach is presented here in order to integrate a pure buoyancy source within the model, based on a volumetric heat generation rate which is uniformly distributed within the heater. Furthermore, detailed experimental–numerical comparisons are given with regard to heat transfer to the walls as well as to heat source behavior and plume characteristics. The results obtained demonstrate that the CFD method employed in this work leads to reliable results. Consequently, this approach can be useful in detailed studies dealing with thermal comfort, indoor air quality and energy consumption for heated rooms. Finally, the simplified method presented here, concerning the integration of the heat source in the CFD model, can be effortlessly extended for other localized heat sources that differ in power, heat emission mode (convection or radiation), shape or size.

Trivariate Isogeometric Analysis for Flexible Multibody Dynamics

Isogeometric analysis (IGA) has been a fundamental step forward in the computational mechanics for the past few years, which maintains the accuracy of the description of computational domain geometry throughout the analysis process. However, the research on IGA in the area of flexible multibody dynamics is little and mainly concentrates on the univariate or bivariate NURBS geometry. This paper applies the trivariate IGA to the flexible multibody dynamics and proposes a continuum mechanics-based method to construct the system dynamic equations within the framework of IGA. A significant feature of this method is that it only employs the position coordinates of the control points as the system variables. To solve the large rotation and deformation coupled problems without introducing any rotation angles, the Green-Lagrange strain tensor is adopted. The evaluation of the elastic force and its Jacobian is easy and accurate by exploiting the appropriate mathematical transformation. In addition, the mass matrix and the generalized gravity force remain constant, and the centrifugal and Coriolis inertia forces equal zero. A numerical experiment is conducted using a thin-plate pendulum, which proves the feasibility and effectiveness of this method.

Non-Newtonian Blood Flow around Healthy and Regurgitated Aortic Valve with Coronary Blood Flow Involved

Most numerical simulations about aortic valve are discussing about the blood flow through prosthetic valves, therefore this study covers a biological aortic valve. In this paper the simulation of blood flow around the regurgitated valve as well as around the health valve have been investigated and is showing how the regurgitation affects the heart function and coronary blood flow. Furthermore it also covers the coronary blood flow and its affect on the blood motion around the valve and consequently on the possible calcification. The physical problem has been treated for the period of closed valve, because of the regurgitation, which occurs at that time. For this restriction the assumption of non-elastic geometry has been used. Also the non-Newtonian Power Law model for the blood rheology has been used; because of the regions of slowly moving blood. Results are showing that the coronary blood flow does not have a high impact on the blood motion and thus the calcification is more probable as well that the regurgitation has a strong affect on the heart function, like aortic pressure drop, increased left ventricle volume, etc. The calcification reason has also been stated, but needs some further investigation. This paper covers in detail the geometry of computational domain and physics, so the results can be easily repeated.

Three-dimensional flow in cavity at yaw

This study introduces a “building block” prototype model of three-dimensional (3-D) flows about protrusions and cavities with an arbitrary angle between the external flow and rigid elements. The considered flow in a 3-D cavity has the lid of cavity moving along the lid diagonal (Case A). The proposed case is taken as a typical representative of essentially 3-D highly separated vortical flows having simple single-block rectangular geometry of computational domain. This 3-D lid-driven cavity flow is studied by numerical solution of the 3-D viscous Navier–Stocks equations using FLUENT software with second-order upwind schemes for convective terms. Computational results are compared to the classical benchmark case where the lid moves in the direction parallel to the cavity side walls (Case B).The volume and plane integrals of momentum in the direction of lid motion and perpendicular to it are introduced to compare cases in a quantitative way. The integral momentum of the secondary flow (transverse to the lid motion) appears to be about an order of magnitude larger than that in Case B. In the proposed flow, the number and strength of secondary vortices depend substantially on the Re number of the flow whereas in Case B only one pair of secondary vortices appears for arbitrary Re number. For a rectangular 3-D 3:1:1 cavity, the integral momentum of the secondary flow in Case A is an order of magnitude larger than that in the Case B. The flowfield in Case A includes a curvilinear separation line and non-symmetrical vortices.