516
Views
0
CrossRef citations to date
0
Altmetric
Research Article

An efficient implementation of compact third-order implicit reconstruction solver with a simple WBAP limiter for compressible flows on unstructured meshes

&
Article: 2249135 | Received 11 Jun 2023, Accepted 12 Aug 2023, Published online: 05 Sep 2023

References

  • Antoniadis, A. F., Drikakis, D., Farmakis, P. S., Fu, L., Kokkinakis, I., Nogueira, X., Silva, P. A. S. F., Skote, M., Titarev, V., & Tsoutsanis, P. (2022). UCNS3D: An open-source high-order finite-volume unstructured CFD solver. Computer Physics Communications, 279, Article 108453. https://doi.org/10.1016/j.cpc.2022.108453
  • Barth, T., & Jespersen, D. (1989, January 9). The design and application of upwind schemes on unstructured meshes. 27th Aerospace Sciences Meeting, Reno, NV, USA. https://doi.org/10.2514/6.1989-366
  • Busto, S., Chiocchetti, S., Dumbser, M., Gaburro, E., & Peshkov, I. (2020). High order ADER schemes for continuum mechanics. Frontiers in Physics, 8, Article 32. https://doi.org/10.3389/fphy.2020.00032
  • Cheng, L., Deng, X., & Xie, B. (2023). An accurate and practical numerical solver for simulations of shock, vortices and turbulence interaction problems. Acta Astronautica, 210, 1–13. https://doi.org/10.1016/j.actaastro.2023.04.049
  • Deng, X. (2023). A unified framework for non-linear reconstruction schemes in a compact stencil. Part 1: Beyond second order. Journal of Computational Physics, 481, Article 112052. https://doi.org/10.1016/j.jcp.2023.112052
  • Deng, X., Massey, J. C., & Swaminathan, N. (2023). Large-eddy simulation of bluff-body stabilized premixed flames with low-dissipative, structure-preserving convection schemes. AIP Advances, 13(5), Article 055014. https://doi.org/10.1063/5.0155829
  • Dong, H., Zhou, T., & Liu, F. (2023). Fully discrete WENO with double entropy condition for hyperbolic conservation laws. Engineering Applications of Computational Fluid Mechanics, 17(1), Article 2145373. https://doi.org/10.1080/19942060.2022.2145373
  • Ferracina, L., & Spijker, M. N. (2008). Strong stability of singly-diagonally-implicit Runge–Kutta methods. Applied Numerical Mathematics, 58(11), 1675–1686. https://doi.org/10.1016/j.apnum.2007.10.004
  • Fu, G., & Shu, C.-W. (2017). A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. Journal of Computational Physics, 347, 305–327. https://doi.org/10.1016/j.jcp.2017.06.046
  • Godunov, S. K. (1959). A difference method for the numerical calculationof discontinuous solutions of hydrodynamic equations. Mat. Sb. (N.S.), 47(3), 271–306.
  • Gottlieb, S., Shu, C.-W., & Tadmor, E. (2001). Strong stability-preserving high-order time discretization methods. SIAM Review, 43(1), 89–112. https://doi.org/10.1137/S003614450036757X
  • Heylmun, J., Vonk, P., & Brewer, T. (n.d.). Blastfoam theory and user guide. Synthetik Applied Technologies, LLC.
  • Hu, C., & Shu, C.-W. (1999). Weighted essentially non-oscillatory schemes on triangular meshes. Journal of Computational Physics, 150(1), 97–127. https://doi.org/10.1006/jcph.1998.6165
  • Jasak, H. (1996). Error analysis and estimation for the finite volume method with applications to fluid flows. Imperial College London (University of London).
  • Ji, Z., Liang, T., & Fu, L. (2022). A class of new high-order finite-volume TENO schemes for hyperbolic conservation laws with unstructured meshes. Journal of Scientific Computing, 92(2), Article 61. https://doi.org/10.1007/s10915-022-01925-5
  • Ji, Z., Liang, T., & Fu, L. (2023). High-order finite-volume TENO schemes with dual ENO-like stencil selection for unstructured meshes. Journal of Scientific Computing, 95(3), Article 76. https://doi.org/10.1007/s10915-023-02199-1
  • Jiang, G.-S., & Shu, C.-W. (1996). Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126(1), 202–228. https://doi.org/10.1006/jcph.1996.0130
  • Krivodonova, L., & Berger, M. (2006). High-order accurate implementation of solid wall boundary conditions in curved geometries. Journal of Computational Physics, 211(2), 492–512. https://doi.org/10.1016/j.jcp.2005.05.029
  • Kurganov, A., & Tadmor, E. (2000). New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. Journal of Computational Physics, 160(1), 241–282. https://doi.org/10.1006/jcph.2000.6459
  • KvarnO, A., Ncrsett, S. P., & Owren, B. (n.d.). Runge-Kutta research in Trondheim, 15.
  • Lax, P. D. (1954). Weak solutions of nonlinear hyperbolic equations and their numerical computation. Communications on Pure and Applied Mathematics, 7(1), 159–193. https://doi.org/10.1002/cpa.3160070112
  • Lax, P. D., & Liu, X.-D. (1998). Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM Journal on Scientific Computing, 19(2), 319–340. https://doi.org/10.1137/S1064827595291819
  • Li, R., Zhao, L., Ge, N., Gao, L., & Ni, M. (2022). Grid resolution assessment method for hybrid RANS-LES in turbomachinery. Engineering Applications of Computational Fluid Mechanics, 16(1), 279–295. https://doi.org/10.1080/19942060.2021.2009917
  • Li, W., & Ren, Y.-X. (2012a). High-order k-exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids. International Journal for Numerical Methods in Fluids, 70(6), 742–763. https://doi.org/10.1002/fld.2710
  • Li, W., & Ren, Y.-X. (2012b). The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids II: Extension to high order finite volume schemes. Journal of Computational Physics, 231(11), 4053–4077. https://doi.org/10.1016/j.jcp.2012.01.029
  • Li, W., Ren, Y.-X., Lei, G., & Luo, H. (2011). The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids. Journal of Computational Physics, 230(21), 7775–7795. https://doi.org/10.1016/j.jcp.2011.06.018
  • Lübon, C., Kessler, M., Wagner, S., & Kramer, E. (2006, June 5). High-order boundary discretization for discontinuous Galerkin codes. 24th AIAA Applied Aerodynamics Conference, San Francisco, California. https://doi.org/10.2514/6.2006-2822
  • Luo, H., Baum, J. D., & Löhner, R. (1998). A fast, matrix-free implicit method for compressible flows on unstructured grids. Journal of Computational Physics, 146(2), 664–690. https://doi.org/10.1006/jcph.1998.6076
  • Luo, H., Baum, J. D., & Löhner, R. (2001). An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids. Computers & Fluids, 30(2), 137–159. https://doi.org/10.1016/S0045-7930(00)00011-6
  • Luo, H., Baum, J. D., & Löhner, R. (2008). A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids. Journal of Computational Physics, 227(20), 8875–8893. https://doi.org/10.1016/j.jcp.2008.06.035
  • Mangani, L., Launchbury, D. R., Casartelli, E., & Romanelli, G. (2015). Development of high order LES solver for heat transfer applications based on the open source OpenFOAM framework. Volume 5B: Heat Transfer, V05BT13A017. https://doi.org/10.1115/GT2015-43279
  • Nielsen, E., Walters, R., Anderson, W., & Keyes, D. (1995, June 19). Application of Newton-Krylov methodology to a three-dimensional unstructured Euler code. 12th Computational Fluid Dynamics Conference, San Diego, CA, USA. https://doi.org/10.2514/6.1995-1733
  • Proskurov, S., Ewert, R., Lummer, M., Mößner, M., & Delfs, J. W. (2022). Sound shielding simulation by coupled discontinuous Galerkin and fast boundary element methods. Engineering Applications of Computational Fluid Mechanics, 16(1), 1690–1705. https://doi.org/10.1080/19942060.2022.2098827
  • Qi, J., Xu, J., Han, K., & Jahn, I. H. J. (2022). Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics. Engineering Applications of Computational Fluid Mechanics, 16(1), 116–140. https://doi.org/10.1080/19942060.2021.2002723
  • Qiu, J., & Shu, C.-W. (2005). A comparison of troubled-cell indicators for Runge–Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. SIAM Journal on Scientific Computing, 27(3), 995–1013. https://doi.org/10.1137/04061372X
  • Shu, C.-W., & Osher, S. (1989). Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. Journal of Computational Physics, 83(1), 32–78. https://doi.org/10.1016/0021-9991(89)90222-2
  • Sod, G. A. (1978). A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of Computational Physics, 27(1), 1–31. https://doi.org/10.1016/0021-9991(78)90023-2
  • Synthetik Applied Technologies, LLC. (2020). blastFoam: A solver for compressible multi-fluid flow with application to high-explosive detonation [Computer software]. https://github.com/synthetik-technologies/blastfoam.
  • Toro, E. F. (2009). Riemann solvers and numerical methods for fluid dynamics (pp. 87–114). Springer. https://doi.org/10.1007/b79761_3
  • Tsoutsanis, P. (2019). Stencil selection algorithms for WENO schemes on unstructured meshes. Journal of Computational Physics: X, 4, Article 100037. https://doi.org/10.1016/j.jcpx.2019.100037
  • Tsoutsanis, P., & Dumbser, M. (2021). Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes. Computers & Fluids, 225, Article 104961. https://doi.org/10.1016/j.compfluid.2021.104961
  • Venkatakrishnan, V. (1995). Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. Journal of Computational Physics, 118(1), 120–130. https://doi.org/10.1006/jcph.1995.1084
  • Vevek, U. S. (2020). Development of high order WENO schemes for large-eddy simulation of compressible flows in OpenFOAM [Nanyang Technological University]. https://doi.org/10.32657/10356/141638
  • Wang, Q., Ren, Y.-X., & Li, W. (2016a). Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes. Journal of Computational Physics, 314, 863–882. https://doi.org/10.1016/j.jcp.2016.01.036
  • Wang, Q., Ren, Y.-X., & Li, W. (2016b). Compact high order finite volume method on unstructured grids II: Extension to two-dimensional Euler equations. Journal of Computational Physics, 314, 883–908. https://doi.org/10.1016/j.jcp.2016.03.048
  • Wang, Q., Ren, Y.-X., Pan, J., & Li, W. (2017). Compact high order finite volume method on unstructured grids III: Variational reconstruction. Journal of Computational Physics, 337, 1–26. https://doi.org/10.1016/j.jcp.2017.02.031
  • Xu, L., Tang, Y., Xu, X., Feng, Y., & Guo, Y. (2017). A high order discontinuous Galerkin method based rans turbulence framework for OpenFOAM. Proceedings of the 2017 2nd International Conference on Communication and Information Systems (pp. 404–408). https://doi.org/10.1145/3158233.3159368
  • Yoon, S., & Jameson, A. (1988). Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations. AIAA Journal, 26(9), 1025–1026. https://doi.org/10.2514/3.10007
  • Zanotti, O., Fambri, F., Dumbser, M., & Hidalgo, A. (2015). Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting. Computers & Fluids, 118, 204–224. https://doi.org/10.1016/j.compfluid.2015.06.020
  • Zhou, T., & Dong, H. (2021). A fourth-order entropy condition scheme for systems of hyperbolic conservation laws. Engineering Applications of Computational Fluid Mechanics, 15(1), 1259–1281. https://doi.org/10.1080/19942060.2021.1955010