Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Brady, Peter T.; Livescu, Daniel

doi:10.1016/j.jcp.2020.109794

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Journal Article · Wed Oct 14 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109794· OSTI ID:1680019

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. Here, a completely new approach, termed TEMO (truncation error matching and optimization), is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles directly allow for the construction of stable 8th To the best of the authors' knowledge, these are the highest orders ever achieved for a cut-cell discretization by a significant margin. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1680019

Alternate ID(s):: OSTI ID: 1810925
OSTI ID: 23203513

Report Number(s):: LA-UR--20-22279

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 426; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (39)

Elafint: a Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries Udaykumar, H. S.; Shyy, W.; Rao, M. M. International Journal for Numerical Methods in Fluids, Vol. 22, Issue 8 https://doi.org/10.1002/(SICI)1097-0363(19960430)22:8<691::AID-FLD371>3.0.CO;2-U	journal	April 1996
Calculation of compressible flows about complex moving geometries using a three-dimensional Cartesian cut cell method Yang, G.; Causon, D. M.; Ingram, D. M. International Journal for Numerical Methods in Fluids, Vol. 33, Issue 8 https://doi.org/10.1002/1097-0363(20000830)33:8<1121::AID-FLD45>3.0.CO;2-H	journal	January 2000
Interface tracking finite volume method for complex solid-fluid interactions on fixed meshes Udaykumar, H. S.; Mittal, R.; Rampunggoon, P. Communications in Numerical Methods in Engineering, Vol. 18, Issue 2 https://doi.org/10.1002/cnm.468	journal	December 2001
A level set approach for computing solutions to inviscid compressible flow with moving solid boundary using fixed Cartesian grids Chung, Meng-Hsuan International Journal for Numerical Methods in Fluids, Vol. 36, Issue 4 https://doi.org/10.1002/fld.32	journal	January 2001
CutFEM: Discretizing geometry and partial differential equations: DISCRETIZING GEOMETRY AND PARTIAL DIFFERENTIAL EQUATIONS Burman, Erik; Claus, Susanne; Hansbo, Peter International Journal for Numerical Methods in Engineering, Vol. 104, Issue 7 https://doi.org/10.1002/nme.4823	journal	December 2014
The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul Journal of Computational Physics, Vol. 108, Issue 2 https://doi.org/10.1006/jcph.1993.1182	journal	October 1993
An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions Pember, Richard B.; Bell, John B.; Colella, Phillip Journal of Computational Physics, Vol. 120, Issue 2 https://doi.org/10.1006/jcph.1995.1165	journal	September 1995
Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids Udaykumar, H. S.; Kan, Heng-Chuan; Shyy, Wei Journal of Computational Physics, Vol. 137, Issue 2 https://doi.org/10.1006/jcph.1997.5805	journal	November 1997
Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters Yee, H. C.; Sandham, N. D.; Djomehri, M. J. Journal of Computational Physics, Vol. 150, Issue 1 https://doi.org/10.1006/jcph.1998.6177	journal	March 1999
An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries Ye, T.; Mittal, R.; Udaykumar, H. S. Journal of Computational Physics, Vol. 156, Issue 2 https://doi.org/10.1006/jcph.1999.6356	journal	December 1999
A Cartesian Grid Embedded Boundary Method for the Heat Equation on Irregular Domains McCorquodale, Peter; Colella, Phillip; Johansen, Hans Journal of Computational Physics, Vol. 173, Issue 2 https://doi.org/10.1006/jcph.2001.6900	journal	November 2001
A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries Udaykumar, H. S.; Mittal, R.; Rampunggoon, P. Journal of Computational Physics, Vol. 174, Issue 1 https://doi.org/10.1006/jcph.2001.6916	journal	November 2001
Compact finite difference schemes with spectral-like resolution Lele, Sanjiva K. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90324-R	journal	November 1992
An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies Quirk, James J. Computers & Fluids, Vol. 23, Issue 1 https://doi.org/10.1016/0045-7930(94)90031-0	journal	January 1994
A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional Cartesian grid Kirkpatrick, M. P.; Armfield, S. W.; Kent, J. H. Journal of Computational Physics, Vol. 184, Issue 1 https://doi.org/10.1016/S0021-9991(02)00013-X	journal	January 2003
A strictly conservative Cartesian cut-cell method for compressible viscous flows on adaptive grids Hartmann, Daniel; Meinke, Matthias; Schröder, Wolfgang Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 9-12 https://doi.org/10.1016/j.cma.2010.05.015	journal	February 2011
An immersed volume method for Large Eddy Simulation of compressible flows using a staggered-grid approach Cecere, D.; Giacomazzi, E. Computer Methods in Applied Mechanics and Engineering, Vol. 280 https://doi.org/10.1016/j.cma.2014.07.018	journal	October 2014
Cartesian cut cell approach for simulating incompressible flows with rigid bodies of arbitrary shape Chung, Meng-Hsuan Computers & Fluids, Vol. 35, Issue 6 https://doi.org/10.1016/j.compfluid.2005.04.005	journal	July 2006
Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template Turner, Jacob M.; Haeri, Sina; Kim, Jae Wook Computers & Fluids, Vol. 138 https://doi.org/10.1016/j.compfluid.2016.08.007	journal	October 2016
High-order, stable, and conservative boundary schemes for central and compact finite differences Brady, P. T.; Livescu, D. Computers & Fluids, Vol. 183 https://doi.org/10.1016/j.compfluid.2018.12.010	journal	April 2019
A Cartesian grid embedded boundary method for the heat equation and Poisson’s equation in three dimensions Schwartz, Peter; Barad, Michael; Colella, Phillip Journal of Computational Physics, Vol. 211, Issue 2 https://doi.org/10.1016/j.jcp.2005.06.010	journal	January 2006
Optimised boundary compact finite difference schemes for computational aeroacoustics Kim, Jae Wook Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2007.01.008	journal	July 2007
A conservative immersed interface method for Large-Eddy Simulation of incompressible flows Meyer, M.; Devesa, A.; Hickel, S. Journal of Computational Physics, Vol. 229, Issue 18 https://doi.org/10.1016/j.jcp.2010.04.040	journal	September 2010
A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions Crockett, R. K.; Colella, P.; Graves, D. T. Journal of Computational Physics, Vol. 230, Issue 7 https://doi.org/10.1016/j.jcp.2010.12.017	journal	April 2011
A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations Seo, Jung Hee; Mittal, Rajat Journal of Computational Physics, Vol. 230, Issue 19 https://doi.org/10.1016/j.jcp.2011.06.003	journal	August 2011
A conservative level-set based method for compressible solid/fluid problems on fixed grids Barton, P. T.; Obadia, B.; Drikakis, D. Journal of Computational Physics, Vol. 230, Issue 21 https://doi.org/10.1016/j.jcp.2011.07.008	journal	September 2011
Code verification for finite volume multiphase scalar equations using the method of manufactured solutions Brady, P. T.; Herrmann, M.; Lopez, J. M. Journal of Computational Physics, Vol. 231, Issue 7 https://doi.org/10.1016/j.jcp.2011.12.040	journal	April 2012
A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method Monasse, L.; Daru, V.; Mariotti, C. Journal of Computational Physics, Vol. 231, Issue 7 https://doi.org/10.1016/j.jcp.2012.01.002	journal	April 2012
An accurate moving boundary formulation in cut-cell methods Schneiders, Lennart; Hartmann, Daniel; Meinke, Matthias Journal of Computational Physics, Vol. 235 https://doi.org/10.1016/j.jcp.2012.09.038	journal	February 2013
A novel concept for the design of immersed interface methods Brehm, C.; Fasel, H. F. Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.01.027	journal	June 2013
A locally stabilized immersed boundary method for the compressible Navier–Stokes equations Brehm, C.; Hader, C.; Fasel, H. F. Journal of Computational Physics, Vol. 295 https://doi.org/10.1016/j.jcp.2015.04.023	journal	August 2015
An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows Schneiders, Lennart; Günther, Claudia; Meinke, Matthias Journal of Computational Physics, Vol. 311 https://doi.org/10.1016/j.jcp.2016.01.026	journal	April 2016
A high-order adaptive Cartesian cut-cell method for simulation of compressible viscous flow over immersed bodies Muralidharan, Balaji; Menon, Suresh Journal of Computational Physics, Vol. 321 https://doi.org/10.1016/j.jcp.2016.05.050	journal	September 2016
Development of immersed boundary computational aeroacoustic prediction capabilities for open-rotor noise Brehm, C.; Barad, M. F.; Kiris, C. C. Journal of Computational Physics, Vol. 388 https://doi.org/10.1016/j.jcp.2019.02.011	journal	July 2019
The convergence rate for difference approximations to mixed initial boundary value problems Gustafsson, Bertil Mathematics of Computation, Vol. 29, Issue 130 https://doi.org/10.1090/S0025-5718-1975-0386296-7	journal	May 1975
Code Verification by the Method of Manufactured Solutions Roache, Patrick J. Journal of Fluids Engineering, Vol. 124, Issue 1 https://doi.org/10.1115/1.1436090	journal	November 2001
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries Almgren, Ann S.; Bell, John B.; Colella, Phillip SIAM Journal on Scientific Computing, Vol. 18, Issue 5 https://doi.org/10.1137/S1064827594273730	journal	September 1997
Immersed Boundary Methods Mittal, Rajat; Iaccarino, Gianluca Annual Review of Fluid Mechanics, Vol. 37, Issue 1 https://doi.org/10.1146/annurev.fluid.37.061903.175743	journal	January 2005
Euler calculations for multielement airfoils using Cartesian grids Clarke, D. Keith; Salas, M. D.; Hassan, H. A. AIAA Journal, Vol. 24, Issue 3 https://doi.org/10.2514/3.9273	journal	March 1986

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Data for: Foundations for High-Order, Conservative Cut-Cell Methods: Stable Discretizations on Degenerate Meshes Brady, Peter https://doi.org/10.17632/x5z98g7mz7 The current record is supplemented by this dataset	dataset	January 2020
Data for: Foundations for High-Order, Conservative Cut-Cell Methods: Stable Discretizations on Degenerate Meshes Brady, Peter https://doi.org/10.17632/x5z98g7mz7.1 The current record is supplemented by this dataset	dataset	January 2020

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

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