A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; McCorquodale, Peter; Colella, Phillip

doi:10.1016/j.compfluid.2015.10.001

Title: A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

Journal Article · Sun Dec 20 00:00:00 EST 2015 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2015.10.001· OSTI ID:1378703

Guzik, Stephen M. ^[1]; Gao, Xinfeng ^[1]; Owen, Landon D. ^[1]; McCorquodale, Peter ^[2]; Colella, Phillip ^[2]

Colorado State Univ., Fort Collins, CO (United States). Computational Fluid Dynamics and Propulsion Lab.
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Applied Numerical Algorithms Group

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231; AC52-07NA27344; EE0006086

OSTI ID:: 1378703

Alternate ID(s):: OSTI ID: 1245246

Journal Information:: Computers and Fluids, Vol. 123, Issue C; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 19 works

Citation information provided by
Web of Science

References (28)

High-order, finite-volume methods in mapped coordinates Colella, P.; Dorr, M. R.; Hittinger, J. A. F. Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2010.12.044	journal	April 2011
A high-order finite-volume method for conservation laws on locally refined grids McCorquodale, Peter; Colella, Phillip Communications in Applied Mathematics and Computational Science, Vol. 6, Issue 1 https://doi.org/10.2140/camcos.2011.6.1	journal	January 2011
Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III Harten, Ami; Engquist, Bjorn; Osher, Stanley Journal of Computational Physics, Vol. 131, Issue 1 https://doi.org/10.1006/jcph.1996.5632	journal	February 1997
Weighted Essentially Non-oscillatory Schemes Liu, Xu-Dong; Osher, Stanley; Chan, Tony Journal of Computational Physics, Vol. 115, Issue 1 https://doi.org/10.1006/jcph.1994.1187	journal	November 1994
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations Liska, Richard; Wendroff, Burton SIAM Journal on Scientific Computing, Vol. 25, Issue 3 https://doi.org/10.1137/S1064827502402120	journal	January 2003
High-order methods for the Euler and Navier–Stokes equations on unstructured grids Wang, Z. J. Progress in Aerospace Sciences, Vol. 43, Issue 1-3 https://doi.org/10.1016/j.paerosci.2007.05.001	journal	January 2007
Local adaptive mesh refinement for shock hydrodynamics Berger, M. J.; Colella, P. Journal of Computational Physics, Vol. 82, Issue 1 https://doi.org/10.1016/0021-9991(89)90035-1	journal	May 1989
A parallel solution-adaptive scheme for ideal magnetohydrodynamics Groth, C.; De Zeeuw, D.; Powell, K. 14th Computational Fluid Dynamics Conference https://doi.org/10.2514/6.1999-3273	conference	February 2013
Numerical simulation of laminar reacting flows with complex chemistry Day, M. S.; Bell, J. B. Combustion Theory and Modelling, Vol. 4, Issue 4 https://doi.org/10.1088/1364-7830/4/4/309	journal	December 2000
Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations Baeza, Antonio; Mulet, Pep International Journal for Numerical Methods in Fluids, Vol. 52, Issue 4 https://doi.org/10.1002/fld.1191	journal	January 2006
ADER-WENO finite volume schemes with space–time adaptive mesh refinement Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo Journal of Computational Physics, Vol. 248 https://doi.org/10.1016/j.jcp.2013.04.017	journal	September 2013
High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems Dumbser, Michael; Hidalgo, Arturo; Zanotti, Olindo Computer Methods in Applied Mechanics and Engineering, Vol. 268 https://doi.org/10.1016/j.cma.2013.09.022	journal	January 2014
Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes Mavriplis, Dimitri J. AIAA Journal, Vol. 28, Issue 2 https://doi.org/10.2514/3.10377	journal	February 1990
A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids Henshaw, William D. Journal of Computational Physics, Vol. 113, Issue 1 https://doi.org/10.1006/jcph.1994.1114	journal	July 1994
A parallel solution – adaptive method for three-dimensional turbulent non-premixed combusting flows Gao, Xinfeng; Groth, Clinton P. T. Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2010.01.001	journal	May 2010
An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems Remacle, Jean-François; Flaherty, Joseph E.; Shephard, Mark S. SIAM Review, Vol. 45, Issue 1 https://doi.org/10.1137/S00361445023830	journal	January 2003
High-order adaptive quadrature-free spectral volume method on unstructured grids Harris, Robert E.; Wang, Z. J. Computers & Fluids, Vol. 38, Issue 10 https://doi.org/10.1016/j.compfluid.2009.06.009	journal	December 2009
Adjoint-Based Adaptive Mesh Refinement for Complex Geometries Nemec, Marian; Aftosmis, Michael; Wintzer, Mathias 46th AIAA Aerospace Sciences Meeting and Exhibit https://doi.org/10.2514/6.2008-725	conference	June 2012
Implicit Finite-Difference Simulation of Flow about Arbitrary Two-Dimensional Geometries Steger, Joseph L. AIAA Journal, Vol. 16, Issue 7 https://doi.org/10.2514/3.7377	journal	July 1978
A High-Resolution Rotated Grid Method for Conservation Laws with Embedded Geometries Helzel, Christiane; Berger, Marsha J.; Leveque, Randall J. SIAM Journal on Scientific Computing, Vol. 26, Issue 3 https://doi.org/10.1137/S106482750343028X	journal	January 2005
A Cartesian grid embedded boundary method for hyperbolic conservation laws Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J. Journal of Computational Physics, Vol. 211, Issue 1 https://doi.org/10.1016/j.jcp.2005.05.026	journal	January 2006
A fourth-order accurate local refinement method for Poisson’s equation Barad, Michael; Colella, Phillip Journal of Computational Physics, Vol. 209, Issue 1 https://doi.org/10.1016/j.jcp.2005.02.027	journal	October 2005
A limiter for PPM that preserves accuracy at smooth extrema Colella, Phillip; Sekora, Michael D. Journal of Computational Physics, Vol. 227, Issue 15 https://doi.org/10.1016/j.jcp.2008.03.034	journal	July 2008
On Conservation at Grid Interfaces Berger, Marsha J. SIAM Journal on Numerical Analysis, Vol. 24, Issue 5 https://doi.org/10.1137/0724063	journal	October 1987
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws Sod, Gary A. Journal of Computational Physics, Vol. 27, Issue 1 https://doi.org/10.1016/0021-9991(78)90023-2	journal	April 1978
The numerical simulation of two-dimensional fluid flow with strong shocks Woodward, Paul; Colella, Phillip Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90142-6	journal	April 1984
Fundamental Algorithms in Computational Fluid Dynamics Pulliam, Thomas H.; Zingg, David W. Springer Cham https://doi.org/10.1007/978-3-319-05053-9	book	January 2014

Cited By (1)

Correction: A Fourth-Order Finite-Volume Method with Adaptive Mesh Refinement for the Multifluid Plasma Model Polak, Scott; Gao, Xinfeng 2018 AIAA Aerospace Sciences Meeting, 2018 AIAA Aerospace Sciences Meeting https://doi.org/10.2514/6.2018-2195.c1	conference	January 2018

Similar Records

A Freestream-Preserving High-Order Finite-Volume Method for Mapped Grids with Adaptive-Mesh Refinement

Conference · Fri Dec 16 00:00:00 EST 2011 · OSTI ID:1378703

Guzik, S; McCorquodale, P; Colella, P

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Journal Article · Mon Mar 28 00:00:00 EDT 2016 · International Journal for Numerical Methods in Fluids · OSTI ID:1378703

Gao, X.; Owen, L. D.; Guzik, S. M. J.

A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids

Journal Article · Tue Nov 01 00:00:00 EDT 2016 · Computers and Mathematics with Applications (Oxford) · OSTI ID:1378703

Guzik, S. M.; Gao, X.; Olschanowsky, C.

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
High-order finite-volume method
Freestream-preserving
Mapped grids
Adaptive-mesh refinement
Finite-volume method
Hyperbolic conservation laws

Title: A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

Citation Formats

References (28)

Cited By (1)

Similar Records

Related Subjects