A Flux Splitting Method for the SHTC Model for High-performance Simulations of Two-phase Flows
In this paper we propose a new flux splitting approach for the symmetric hyperbolic thermodynamically compatible (SHTC) equations of compressible two-phase flow which can be used in finite-volume methods. The approach is based on splitting the entire model into acoustic and pseudo-convective submodels. The associated acoustic system is numerically solved applying HLLC-type Riemann solver for its Lagrangian form. The convective part of the pseudo-convective submodel is solved by a standart upwind scheme. For other parts of the pseudo-convective submodel we apply the FORCE method. A comparison is carried out with unsplit methods. Numerical results are obtained on several test problems. Results show good agreement with exact solutions and reference calculations.
Baer, M., Nunziato, J.: A Two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. International Journal of Multiphase Flow 12(6), 861–889 (1986), DOI: 10.1016/0301-9322(86)90033-9
ten Eikelder, M.F.P., Daude, F., Koren, B., Tijsseling, A.S.: An acoustic-convective splittingbased approach for the Kapila two-phase flow model. Journal of Computational Physics 331, 188–208 (2017), DOI: 10.1016/j.jcp.2016.11.031
Kapila, A., Menikoff, R., Bdzil, J., Son, S., Stewart, D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations. Physics of Fluids 13(10), 3002–3024 (2001), DOI: 10.1063/1.1398042
Romenski, E., Drikakis, D., Toro, E.F.: Conservative models and numerical methods for compressible two-phase flow. Journal of Scientific Computing 42(1), 68–95 (2010), DOI: 10.1007/s10915-009-9316-y
Sadovnichy, V., Tikhonravov, A., Voevodin, Vl., Opanasenko, V.: ”Lomonosov”: Supercomputing at Moscow State University. In: Contemporary High Performance Computing: FromPetascale toward Exascale. pp. 283–307. Chapman & Hall/CRC Computational Science, CRC Press, Boca Raton, United States, (2013)
Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer (2009), DOI: 10.1007/b79761
Toro, E.F., Spruce, M., Speares, W.: Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4(1), 25–34 (1994), DOI: 10.1007/bf01414629
Toro, E.F., Titarev, V.A.: MUSTA fluxes for systems of conservation laws. Journal of Computational Physics 216(2), 403–429 (2006), DOI: 10.1016/j.jcp.2005.12.012
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