Finite-volume WENO scheme for viscous compressible multicomponent flows

• Published in: Journal of computational physics Vol. 274; pp. 95 - 121
• Main Authors: Coralic, Vedran, Colonius, Tim
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.10.2014
• Subjects: Algorithms; Compressibility; Construction; HLLC; Interface-capturing; Mathematical analysis; Mathematical models; Multicomponent flows; Navier-Stokes equations; Numerical analysis; Shock-capturing; Three dimensional; Viscous; WENO; Viscous; Shock-capturing; HLLC; Interface-capturing; Multicomponent flows; WENO; shock-capturing; multicomponent flows; viscous; interface-capturing
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2014.06.003

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.