Finite-volume WENO scheme for viscous compressible multicomponent flows
- Creators
- Coralic, Vedran
- Colonius, Tim
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.
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.Attached Files
Accepted Version - nihms606496.pdf
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Additional details
- PMCID
- PMC4122134
- Eprint ID
- 49575
- DOI
- 10.1016/j.jcp.2014.06.003
- Resolver ID
- CaltechAUTHORS:20140911-085308346
- NIH
- PO1-DK043881
- NSF
- OCI-1053575
- Created
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2014-09-11Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field