**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

doi: 10.17586/2226-1494-2017-17-5-896-902

doi: 10.17586/2226-1494-2017-17-5-896-902

# FEATURES OF DIFFERENCE SCHEME WITH CUSTOMIZABLE DISSIPATIVE PROPERTIES IN CASE OF TWO-DIMENSIONAL GAS AND GAS-PARTICLE DYNAMICS PROBLEMS

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**Article in**Russian

**For citation:**Sadin D.V., Odoev S.A. Features of difference scheme with customizable dissipative properties in case of two-dimensional gas and gas-particle dynamics problems.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*

*, 2017, vol. 17, no. 5, pp. 896–902 (in Russian). doi: 10.17586/2226-1494-2017-17-5-896-902*

**Abstract**
**Subject of Research.**The paper presents testing results of difference scheme with customizable dissipative properties in the case of the two-dimensional problems for both gas dynamics and gas-suspensions mechanics. **Method.** The second order difference scheme is created with splitting of physical processes into two phases. The first phase uses the central difference, the scalar version of the nonlinear artificial viscosity limiters and semi implicit approximation of the interphase interactions. Reconstructions of TVD type are used at the second phase. **Main Results.** Testing was performed for problems with strong discontinuities when the shock waves interact with suspended particles. For illustrative test problems, the scheme with customizable dissipative properties has demonstrated a good quality of numerical solutions at the level of the WENO5 scheme with the ability to resolve fine details of the flow in case of multiple interactions of shock waves, contact discontinuities and rarefaction waves. Possible oscillations of the numerical solution in the proposed scheme are suppressed by setting its dissipative properties. **Practical Relevance.** The scheme with customizable dissipative properties is the basis for the development of applied software package as a justification tool for the attainable level of technical solutions with the use of the gas suspensions flows.

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1. Le VequeR.J.
2. ToroE.F.
3. VolkovK.N., Deryugin Yu.N., Emel'yanov V.N., Kozelkov A.S., Teterina I.V.
4. NigmatulinR.I.
5. GidaspowD.
6. CroweC.T., Schwarzkopf J.D., Sommerfeld M., Tsuji Y.
7. HudsonJ., Harris D. A high resolution scheme for Eulerian gas–solid two-phase isentropic flow.
8. SadinD.V. A modified large-particle method for calculating unsteady gas flows in a porous medium.
9. SadinD.V. A method for computing heterogeneous wave flows with intense phase interaction.
10. SadinD.V. On the convergence of a certain class of difference schemes for the equations of unsteady gas motion in a disperse medium.
11. SadinD.V. Stiffness problem in modeling wave flows of heterogeneous media with a threetemperature scheme of interphase heat and mass transfer.
12. SaurelR., Le Metayer O., Massoni J., Gavrilyuk S. Shock jump relations for multiphase mixtures with stiff mechanical relaxation.
13. SurovV.S. Hyperbolic models in the mechanics of heterogeneous media.
14. ToroE.F. Riemann-problem based techniques for computing reactive two-phase flows.
15. SaurelR., Abgrall R. A multiphase Godunov method for compressible multifluid and multiphase flows.
16. TokarevaS.A., Toro E.F. HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow.
17. BulatP.V., Volkov K.N., Ilyina T.Y. Interaction of a shock wave with a cloud of particles.
18. SadinD.V. TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type.
19. ChristiansenR.B. Godunov Methods on a Staggered Mesh - An Improved Artificial Viscosity.
20. BensonD.J., Schoenfeld S. A total variation diminishing shock viscosity.
21. CaramanaJ., Shashkov M.J., Whalen P.P. Formulations of artificial viscosity for multi-dimensional shock wave computations.
22. HirschC.
23. FringerO.B., Armfield S.W., Street R.L. Reducing numerical diffusion in interfacial gravity wave simulations.
24. LiskaR., Wendroff B. Comparison of several difference schemes on 1D and 2D test problems for the Euler equations.
LiskaR., Wendroff B. Comparison of several difference schemes on 1D and 2D test problems for the Euler equations.

~liska/CompareEuler/compare8.pdf

**Keywords:**gas dynamics, gas-particle mixture, numerical simulation, test problems, dissipative properties, stability

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~liska/CompareEuler/compare8.pdf