Finite-volume WENO scheme for viscous compressible multicomponent flows

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, a...

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Veröffentlicht in:Journal of computational physics. - 1998. - 274(2014) vom: 01. Okt., Seite 95-121
1. Verfasser: Coralic, Vedran (VerfasserIn)
Weitere Verfasser: Colonius, Tim
Format: Aufsatz
Sprache:English
Veröffentlicht: 2014
Zugriff auf das übergeordnete Werk:Journal of computational physics
Schlagworte:Journal Article HLLC WENO interface-capturing multicomponent flows shock-capturing viscous
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245 1 0 |a Finite-volume WENO scheme for viscous compressible multicomponent flows 
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520 |a 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 
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700 1 |a Colonius, Tim  |e verfasserin  |4 aut 
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