Raghurama Rao Suswaram
Indian Institute of Science, Aerospace Engineering, Faculty Member
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In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to characterize the parameters of the scheme that guarantee... more
In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to characterize the parameters of the scheme that guarantee the preservation of the non-negativity of the particle distribution functions. In the context of the relative velocity schemes, we derive necessary and sufficient conditions for the non-negativity preserving property. These conditions are then expressed in a simple way when the relative velocity is reduced to zero. For the general case, we propose some simple necessary conditions on the relaxation parameters and we put in evidence numerically the non-negativity preserving regions. Numerical experiments show finally that no oscillations occur for the propagation of a non-smooth profile if the non-negativity preserving property is satisfied.
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Using the framework of a Relaxation System, which converts a non-linear conservation law into a system of linear convection equations with non-linear source terms, an accurate shock capturing algorithm is developed for the numerical... more
Using the framework of a Relaxation System, which converts a non-linear conservation law into a system of linear convection equations with non-linear source terms, an accurate shock capturing algorithm is developed for the numerical simulation of hyperbolic conservation equations. The basic idea is to formulate a nite volume method with open coecients of numerical dissipation for the discrete Boltzmann equation and compare the resulting relaxed scheme with Rankine-Hugoniot condition for xing the coecients of numerical dissipation. Since the Rankine-Hugoniot condition is satised by the discretized scheme, the steady discontinuities are captured exactly, like Roe’s approximate Riemann solver. The features of this Accurate Shock Capturing Algorithm with a Relaxation System (ASCARS) are demonstrated by applying it to some standard bench-mark problems.
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ABSTRACT A new upwind Boltzmann scheme termed Peculiar Velocity based Upwind (PVU) method is developed for solving Euler equations. Upwinding is done based on peculiar velocity of Kinetic Theory of Gases. This new method is more efficient... more
ABSTRACT A new upwind Boltzmann scheme termed Peculiar Velocity based Upwind (PVU) method is developed for solving Euler equations. Upwinding is done based on peculiar velocity of Kinetic Theory of Gases. This new method is more efficient and physically more meaningful than its predecessor, the Kinetic Flux Vector Splitting (KFVS) method. The PVU method is applied to some standard test problems. The results demonstrate the soundness of the new idea. The motivation for this work came from the idea of improving the Kinetic Flux Vector Splitting (KFVS) method [1] which was demonstrated to be very robust by its application to a wide variety of 2-D and 3-D problems using structured and unstructured meshes [2,3,4,5]. In the KFVS method upwinding is done based on whether molecular velocity is greater or less than zero. Here, a new upwind Boltzmann scheme, in which upwinding is done based on peculiar velocity, which is the relative velocity of the molecule with respect to the fluid, is presented. The upwind method for Euler equations is obtained by taking moments of the upwind scheme applied to the Boltzmann equation of Kinetic Theory of Gases.
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... Using Peculiar Velocity Based Upwind (PVU) Method MZDauhoo 1, SVRaghurama Rao 2,4, V.Ramesh 3 and SMDeshpande 4 1Dept. ... E-mail : raghu@itwm.uni-kl.de 3National Aerospace Laboratories, PB 1779, Bangalore-560 017, India. E-mail :... more
... Using Peculiar Velocity Based Upwind (PVU) Method MZDauhoo 1, SVRaghurama Rao 2,4, V.Ramesh 3 and SMDeshpande 4 1Dept. ... E-mail : raghu@itwm.uni-kl.de 3National Aerospace Laboratories, PB 1779, Bangalore-560 017, India. E-mail : vramesh @aero. iisc. ...
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This paper introduces a new hybrid shape optimization method using Genetic Algorithm (GA) and Ant Colony Optimization (ACO) coupled with a meshless Computational Fluid Dynamics (CFD) solver. This method converges faster to a better... more
This paper introduces a new hybrid shape optimization method using Genetic Algorithm (GA) and Ant Colony Optimization (ACO) coupled with a meshless Computational Fluid Dynamics (CFD) solver. This method converges faster to a better optimum compared to GA-CFD or ...
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Research Interests: Engineering, Mathematics, Numerical Analysis, Numerical Methods, Numerical Method, and 14 morePhysical sciences, Sound and Vibration, Linear System, Historic conservation law, Finite Difference, Finite Difference Method, Finite Volume Method, Differential equation, Shock Wave, Hyperbolic Conservation Laws, Nonstandard Finite Difference Methods, Exact solution methods, Relaxation Scheme, and Finite Difference Scheme
Research Interests: Engineering, Mathematics, Computer Science, Computational Physics, Nonlinear hyperbolic equations, and 13 moreNumerical Methods, Numerical Method, Shock Waves, Mathematical Sciences, Gas Dynamics, Physical sciences, Solver, Historic conservation law, Finite Volume Method, Shallow Water Equation (SWE), Two Dimensions, Burgers equation, and Euler Equation
Research Interests: Engineering, Mathematics, Computer Science, Computational Physics, Computational Fluid Dynamics, and 12 moreNonlinear hyperbolic equations, Numerical Methods, Numerical Method, Numerical Simulation, Mathematical Sciences, Physical sciences, Euler Equations, Solver, Numerical methods for CFD, Numerical Diffusion, Euler Method, and Kinetic Scheme
Research Interests: Engineering, Mathematics, Physics, Computational Physics, Computational Fluid Dynamics, and 11 moreNavier-Stokes Equations, Mathematical Sciences, Computation Fluid Dynamics, Physical sciences, Lattice Boltzmann method for fluid dynamics, Lattice Boltzmann Method, Boltzmann equation, DDC, Numerical Solution, Kinetic Schemes, and Kinetic Scheme
Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convectiondiffusion equations with nonlinear source terms, a finite variable difference method is developed for... more
Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convectiondiffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolicparabolic equations. ...
Research Interests: Engineering, Computer Science, Algorithms, Computational Physics, Computational Fluid Dynamics, and 15 moreFinite Volume Methods, Mathematical Sciences, Mathematical Analysis, Conservation Laws, Hyperbolic Equations, Mathematical Model, Linear Systems, Finite Difference, Finite Difference Method, Finite Volume Method, Calculation, Convection Diffusion Equation, Hyperbolic Partial Differential Equation, Finite Difference Scheme, and FTCS scheme
Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction... more
Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. A parametric study is performed by varying the Grashof number, aspect ratio, and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the variation of several quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number, and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The average Nusselt number from the conjugate analysis is found to be between the Nusselt numbers of the isothermal and the isoflux cases. The average Nusselt numbers on t...
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An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different... more
An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (ε) to time step. The coarse mesh results obtained with a relaxation scheme are
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... [8]. The total mass constraint is used to determine the zeroth order pressure as follows: (12) View the MathML source where M ≡ M / (ρ c L c 3 ) is the dimensionless total mass and the limits of the integrals are chosen to cover the... more
... [8]. The total mass constraint is used to determine the zeroth order pressure as follows: (12) View the MathML source where M ≡ M / (ρ c L c 3 ) is the dimensionless total mass and the limits of the integrals are chosen to cover the fluid region. ...
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A grid-free central scheme for inviscid compressible flows is presented here. The space derivatives in the governing equations are discretized using the least squares minimization of the error in a Taylor series approximation. The... more
A grid-free central scheme for inviscid compressible flows is presented here. The space derivatives in the governing equations are discretized using the least squares minimization of the error in a Taylor series approximation. The discretization is for any arbitrary cloud of points with full stencil support. A new grid-free central scheme is formulated based on convective - pressure splitting using the mid-points of the lines connecting each point to its neighbours for introducing artificial viscosity. The numerical dissipation is reduced due to the modified eigenvalues in the convective - pressure splitting together with a diusion regulator based on the jump in the Mach number. The results obtained for standard test cases in two dimensions with first and second order accuracy are presented.
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... U. Mohan Varma*, SV Raghurama Rao*, and SM Deshpande* *AR & DB Centre of Excellence for Aerospace CFD, Department of Aerospace Engineering, Indian Institute of Science, Bangalore - 560012, India e-mails: mvarma@aero.iisc.ernet.in,... more
... U. Mohan Varma*, SV Raghurama Rao*, and SM Deshpande* *AR & DB Centre of Excellence for Aerospace CFD, Department of Aerospace Engineering, Indian Institute of Science, Bangalore - 560012, India e-mails: mvarma@aero.iisc.ernet.in, raghu@aero.iisc.ernet.in ...
... The ACO-IM problem can be described as follows. Let g(/3) : D => R be Page 2. 2 GN SashiKumar, AK Mahendra and SV Raghurama Rao a continuous and bounded function and /? ... Page 4. GN Sashi Kumar, AK Mahendra and SV Raghurama Rao... more
... The ACO-IM problem can be described as follows. Let g(/3) : D => R be Page 2. 2 GN SashiKumar, AK Mahendra and SV Raghurama Rao a continuous and bounded function and /? ... Page 4. GN Sashi Kumar, AK Mahendra and SV Raghurama Rao 10-1 o1 ...
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equations. The proposed scheme performs better than the original... more
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equations. The proposed scheme performs better than the original SUPG stabilized method in multi-dimensions. To demonstrate the numerical accuracy of the scheme, various numerical experiments have been carried out for 1D and 2D Burgers equation as well as for 1D and 2D Euler equations using Q4 and T3 elements. Furthermore, spectral stability analysis is done for the explicit 2D formulation. Finally, a comparison is made between explicit and implicit versions of the KSUPG scheme.
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the govening equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as... more
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the govening equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as a discrete velocity Boltzmann system. As a result of this interpretation, the local equilibrium distribution functions are simple algebraic functions of the conserved variables and the fluxes, without the low Mach number expansion present in the equilibrium distribution of the traditional Lattice Boltz-mann Method (LBM). This new Lattice Boltzmann Relaxation Scheme (LBRS) thus overcomes the low Mach number limitation and can successfully simulate compressible flows. While doing so, our algorithm retains all the distinctive features of the traditional LBM. Numerical simulations carried out for inviscid flows in one and two dimensions show that the method can simulate the features of compressible flows like shock waves and expansion waves.
An exact discontinuity capturing central solver developed recently, named MOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks, JCP, 228 (3) (2009) 770–798), is analyzed and improved further to make it entropy stable.... more
An exact discontinuity capturing central solver developed recently, named MOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks, JCP, 228 (3) (2009) 770–798), is analyzed and improved further to make it entropy stable. MOVERS, which is designed to capture steady shocks and contact discontinuities exactly by enforcing the Rankine-Hugoniot jump condition directly in the discretization process, is a low diffusive algorithm in a simple central discretization framework, free of complicated Riemann solvers and flux splittings. However, this algorithm needs an entropy fix to avoid nonsmoothness in the expansion regions. The entropy conservation equation is used as a guideline to introduce an optimal numerical diffusion in the smooth regions and a limiter based switchover is introduced for numerical diffusion based on jump conditions at the large gradients. The resulting new scheme is entropy stable, accurate and captures steady discontinuities exactly while avoiding an entropy fix.
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A simple and accurate central scheme in finite volume framework is developed for systems of hyperbolic conservation laws, using a splitting of strongly hyperbolic and weakly hyperbolic parts. This leads to the flux function of 1D inviscid... more
A simple and accurate central scheme in finite volume framework is developed for systems of hyperbolic conservation laws, using a splitting of strongly hyperbolic and weakly hyperbolic parts. This leads to the flux function of 1D inviscid Euler compressible system being split into convection and pressure parts and 1D inviscid shallow water system into convection and celerity parts. The numerical diffusion is fixed based on flux equivalence principle, which leads to the satisfaction of the jump conditions. The numerical scheme is tested on various shock tube problems of gas dynamics for 1D Euler equations and on dam breaking problems for shallow water equations. Comparison is done with an approximate Riemann solver to demonstrate the efficiency of the numerical method. Keywords: Central solver, Weak–strong hyperbolic splitting, Convection–pressure splitting, Convection– celerity splitting, Exact capturing of steady discontinuities without entropy fixes
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A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple... more
A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical method. The basic idea is to fix the coefficient of numerical dissipation based on the Rankine-Hugoniot (jump) condition. Several numerical examples for scalar and vector hyperbolic conservation laws representing the inviscid Burgers equation, the Euler equations of gas dynamics, shallow water equations and ideal MHD equations in one and two dimensions are presented which demonstrate the efficiency and accuracy of this numerical method in capturing the flow features.
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A diffusion regulation parameter, which operates based on the jump in the Mach number, is presented for implementation in Euler solvers. This diffusion regulation parameter adjusts itself automatically in different regimes of the flow... more
A diffusion regulation parameter, which operates based on the jump in the Mach number, is presented for implementation in Euler solvers. This diffusion regulation parameter adjusts itself automatically in different regimes of the flow and leads to the exact capturing of steady contact discontinuities which are aligned with the grid-lines. This diffusion regulator parameter reduces numerical dissipation, is very simple and can be easily incorporated in any Euler solver. By coupling such a parameter with a simple numerical method like the Local Lax-Friedrichs (Rusanov) method, an accurate and yet simple numerical method is developed for the numerical simulation of inviscid compressible fluid flows. To demonstrate the applicability of this approach to any Euler solver, the diffusion regulation parameter is also applied in the framework of a Kinetic Scheme which is very diffusive and the improvements in the accuracy for both the methods are demonstrated through several bench-mark test problems.
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An implicit sub-grid scale model for large eddy simulation is presented by utilizing the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady... more
An implicit sub-grid scale model for large eddy simulation is presented by utilizing the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations with varying the ratio of relaxation parameter to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a of fourth order CWENO discretization in space and third order TVD Runge-Kutta discretization in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.
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Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for... more
Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai, for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.
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A new Grid-free Upwind Relaxation Scheme for simulating inviscid compressible flows is presented in this paper. The non-linear conservation equations are converted to linear convection equations with non-linear source terms by using a... more
A new Grid-free Upwind Relaxation Scheme for simulating inviscid compressible flows is presented in this paper. The non-linear conservation equations are converted to linear convection equations with non-linear source terms by using a Relaxation System and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least Squares Upwinding is used for discretizing the convection equations, thus developing a grid-free scheme which can operate on any arbitrary distribution of points. The scheme is grid-free in the sense that it works on any arbitrary distribution of points and it doesn't require any topological information like elements, faces, edges etc. This method is tested on some standard test cases. To explore the power of the grid-free scheme, solution based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid-free scheme.
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The relation between the lattice Boltzmann method, which has recently become popular, and the kinetic schemes, which are routinely used in computational fluid dynamics, is explored. A new discrete velocity method for the numerical... more
The relation between the lattice Boltzmann method, which has recently become popular, and the kinetic schemes, which are routinely used in computational fluid dynamics, is explored. A new discrete velocity method for the numerical simulation of Navier-Stokes equations for incompressible fluid flow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the lattice Boltzmann method.
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Non-standard finite difference methods (NSFDM) introduced by Mickens are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods... more
Non-standard finite difference methods (NSFDM) introduced by Mickens are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear
hyperbolic conservation laws, these methods reproduce exact
solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to non-linear scalar hyperbolic conservation laws. The original non-standard finite difference methods introduced by Mickens were not in conservation form, which is an important feature in capturing discontinuities at the right
locations. Mickens recently introduced a non-standard finite difference method in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes in which the accurate non-standard finite difference method is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin are based on relaxation systems which replace the non-linear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter is
chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.
hyperbolic conservation laws, these methods reproduce exact
solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to non-linear scalar hyperbolic conservation laws. The original non-standard finite difference methods introduced by Mickens were not in conservation form, which is an important feature in capturing discontinuities at the right
locations. Mickens recently introduced a non-standard finite difference method in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes in which the accurate non-standard finite difference method is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin are based on relaxation systems which replace the non-linear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter is
chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.
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In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method can be easily extended to any complex system of conservation laws. The numerical scheme is based on a... more
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method can be easily extended to any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. The first order accurate method is conservative, preserves the positivity of mass density and pressure and entropy stable. An anti-diffusive Chapman-Enskog distribution is used to derive a second order accurate method. The results of numerical experiments on some benchmark problems confirm the efficiency and robustness of the proposed scheme.
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A new upwind method called Peculiar Velocity based Upwind (PVU) method is developed for obtaining the numerical solution of the Euler equations of gas dynamics. It is based on the concept of peculiar velocity of Kinetic Theory of Gases.... more
A new upwind method called Peculiar Velocity based Upwind (PVU) method is developed for obtaining the numerical solution of the Euler equations of gas dynamics. It is based on the concept of peculiar velocity of Kinetic Theory of Gases. This method is physically more meaningful and more efficient than its predecessor, the Kinetic Flux Vector Splitting method. This new method is tested on a variety of test problems on structured meshes and unstructured meshes with mesh refinement. The results demonstrate the robustness of the method and further establish its capability in capturing various flow features.