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Finite-volume WENO scheme for viscous compressible multicomponent flows

Coralic, Vedran and Colonius, Tim (2014) Finite-volume WENO scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274 . pp. 95-121. ISSN 0021-9991. PMCID PMC4122134. doi:10.1016/

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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.

Item Type:Article
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URLURL TypeDescription CentralArticle
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2014 Elsevier Inc. Received 11 January 2014; Received in revised form 6 May 2014; Accepted 2 June 2014; Available online 5 June 2014. The authors are thankful for the insightful discussions with Eric Johnsen, Daniel Appelö, Vladimir Titarev and Chi-Wang Shu. The work was supported by the National Institutes of Health under grant PO1-DK043881. The three-dimensional computations presented here utilized the Extreme Science and Engineering Discovery Environment, which is supported by the National Science Foundation grant number OCI-1053575.
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Subject Keywords:WENO; HLLC; Viscous; Shock-capturing; Interface-capturing; Multicomponent flows
PubMed Central ID:PMC4122134
Record Number:CaltechAUTHORS:20140911-085308346
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Official Citation:Vedran Coralic, Tim Colonius, Finite-volume WENO scheme for viscous compressible multicomponent flows, Journal of Computational Physics, Volume 274, 1 October 2014, Pages 95-121, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49575
Deposited By: Tony Diaz
Deposited On:11 Sep 2014 16:00
Last Modified:10 Nov 2021 18:46

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