Designing an Efficient Solution Strategy for Fluid Flows

Gerritsen, Margot; Olsson, Pelle

doi:10.1006/jcph.1996.0248

Cited by 77 publications

(55 citation statements)

References 10 publications

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“…It requires the use of entropy variables in the evaluation of the flux, although the standard conservative variables are updated at each time step. There is some latitude in the definition of the generalized entropy function h(u) of the state vector u. Harten [13] [14], and also by Gerritsen and Olsson [15], who proposed a non conservative entropy preserving scheme.…”

Section: Introductionmentioning

confidence: 99%

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Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-Dimensional Viscous Compressible Flow in a Shock Tube Using Entropy and Kinetic Energy Preserving Schemes

2007

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This paper follows up on the author's recent paper "The Construction of Discretely Conservative Finite Volume Schemes that also Globally Conserve Energy or Enthalpy".In the case of the gas dynamics equations the previous formulation leads to an entropy preserving (EP) scheme. It is shown in the present paper that it is also possible to construct the flux of a conservative finite volume scheme to produce a kinetic energy preserving (KEP) scheme which exactly satisfies the global conservation law for kinetic energy. A proof is presented for three dimensional discretization on arbitrary grids.Both the EP and KEP schemes have been applied to the direct numerical simulation of one-dimensional viscous flow in a shock tube. The computations verify that both schemes can be used to simulate flows with shock waves and contact discontinuities without the introduction of any artificial diffusion. The KEP scheme performed better in the tests.2

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Section: Introductionmentioning

confidence: 99%

“…Different choices of the entropy function g(s) have been discussed by Harten [13], Hughes, Franca and Mallet [14], and Gerritsen and Olsson [15].…”

Section: Introductionmentioning

confidence: 99%

Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-Dimensional Viscous Compressible Flow in a Shock Tube Using Entropy and Kinetic Energy Preserving Schemes

2007

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“…In fact, the change of variable u to w is used to create symmetric variables for smoothing the solution. Entropy variables have been studied by Hughes, Franca and Mallet [15] and also by Gerritsen and Olsson [16].…”

Section: Introductionmentioning

confidence: 99%

Analysis of One-Dimensional Inviscid and Two-Dimensional Viscous Flows Using Entropy Preserving Method

2014

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In this paper, the entropy preserving (EP) scheme (which is introduced recently by Jameson) has been considered deeply and compared with the other artificial viscosity and upwind schemes. The discretization of the governing equations in the EP scheme is performed in such a way that the entropy is conserved in all those points with no shock. The purpose of this study was to introduce a stable numerical method that enters a minimum artificial dissipation only in the vicinity of shocks. In this paper, an inviscid one-dimensional flow through a convergent-divergent nozzle and a viscous two-dimensional flow with axial symmetry are considered. It is shown that the EP scheme is more accurate if the number of mesh points is increased; and in contrast to other schemes, there is no limit in increasing the number of points.

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“…with cri,j a positive definite matrix and h = Ax the fixed grid spacing, we have the property BjSrn SjSgreen and H. C. Yee for entropy splitting of a perfect gas case are given in [2], and for a thermally perfect gas case are given in [16]. The above entropy splitting was used in a numerical method in [2], where the semi-discrete approximation was written as…”

mentioning

confidence: 99%

“…The above entropy splitting was used in a numerical method in [2], where the semi-discrete approximation was written as…”

mentioning

confidence: 99%

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

Sjögreen

Yee

2003

Hyperbolic Problems: Theory, Numerics, Applications

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Designing an Efficient Solution Strategy for Fluid Flows

Cited by 77 publications

References 10 publications

Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-Dimensional Viscous Compressible Flow in a Shock Tube Using Entropy and Kinetic Energy Preserving Schemes

Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-Dimensional Viscous Compressible Flow in a Shock Tube Using Entropy and Kinetic Energy Preserving Schemes

Analysis of One-Dimensional Inviscid and Two-Dimensional Viscous Flows Using Entropy Preserving Method

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

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