title: Finite-volume WENO scheme for viscous compressible multicomponent flows.
abstract: 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.
authors.affiliation: Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Vedran
authors.initials: V
authors.lastname: Coralic
authors.affiliation: Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Tim
authors.initials: T
authors.lastname: Colonius
keywords: HLLC; WENO; interface-capturing; multicomponent flows; shock-capturing; viscous
references.citation: J Acoust Soc Am. 2008 May;123(5):2867-74
references.pmid: 18529202
references.citation: J Acoust Soc Am. 2009 Nov;126(5):2746-56
references.pmid: 19894850
references.citation: Urol Res. 2010 Aug;38(4):321-6
references.pmid: 20680255
references.citation: Eur J Mech B Fluids. 2013 Jul;40:64-74
references.pmid: 24015027