Finite-volume WENO scheme for viscous compressible multicomponent flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Coralic, Vedran¹  Colonius, Tim¹ 

[1] CALTECH, Div Engn & Appl Sci, Pasadena, CA 91125 USA

关键词: WENO;    HLLC;    Viscous;    Shock-capturing;    Interface-capturing;    Multicomponent flows;   

DOI  :  10.1016/j.jcp.2014.06.003

来源: Elsevier

【 摘 要 】

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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