2,023
Views
1
CrossRef citations to date
0
Altmetric
Articles

An ALE formulation for compressible flows based on multi-moment finite volume method

, &
Pages 791-809 | Received 02 Jul 2018, Accepted 20 Sep 2018, Published online: 10 Oct 2018

References

  • Ahn H. T., & Kallinderis Y. (2006). Strongly coupled flow/struc-ture interactions with a geometrically conservative ALE scheme on general hybrid meshes. Journal of Computational Physics, 219(2), 671–696. doi: 10.1016/j.jcp.2006.04.011
  • Akbarian E., Najafi B., Jafari M., Aedabili S. F., Shamshirband S., & Chau K.-w. (2018). Experimental and computational fluid dynamics-based numerical simulation of using natural gas in a dual-fueled diesel engine. Engineering Applications of Computational Fluid Mechanics, 12(1), 517–534. doi: 10.1080/19942060.2018.1472670
  • Anagnostopoulos P. (2000). Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 1: Lock-in zone, hydrodynamic forces and wake geometry. Journal of Fluids and Structures, 14(6), 819–851. doi: 10.1006/jfls.2000.0302
  • Ardabili S.F., Najafi B., Shamshirband S., Bidgoli B., Deo R. C., & Chau K.-w. (2018). Computational intelligence approach for modeling hydrogen production: A review. Engineering Applications of Computational Fluid Mechanics, 12(1), 438–458. doi: 10.1080/19942060.2018.1452296
  • Bazilevs, Y., Takizawa, K., & Tezduyar, T. E. (2013). Computational fluid-structure interaction: Methods and applications. San Diego, CA: John Wiley & Sons.
  • Bos F. M. (2010). Numerical simulations of flapping foil and wing aerodynamics: Mesh deformation using radial basis functions (Doctoral dissertation).
  • Boscheri W., & Dumbser M. (2014). A direct Arbitrary-Lagrangian Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D. Journal of Computational Physics, 275, 484–523. doi: 10.1016/j.jcp.2014.06.059
  • Boscheri W., & Dumbser M (2013). Arbitrary-Lagrangian-Eulerian one-step WENO finite volume schemes on unstructured triangular meshes. Communications in Computational Physics, 14(5), 1174–1206. doi: 10.4208/cicp.181012.010313a
  • Boscheri W., Dumbser M., & Zanotti O. (2015). High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes. Journal of Computational Physics, 291, 120–150. doi: 10.1016/j.jcp.2015.02.052
  • Boscheri W., Loubére R., & Dumbser M. (2015). Direct Arbitrary-Lagrangian Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws. Journal of Computational Physics, 292, 56–87. doi: 10.1016/j.jcp.2015.03.015
  • Carlson, J. (2011). Inflow/outflow boundary conditions with application to FUN3D. NASA Langley Research Center, Hampton, VA. NASA/TM-2011-217181, L-20011, NF1676L-12459.
  • Cheng J., & Shu C.-W. (2008). A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations. Communications in Computational Physics, 4, 1008–1024.
  • Cheng J., & Shu C.-W. (2007). A high order ENO conservative Lagrangian type scheme for the compressible Euler equations. Journal of Computational Physics, 227(2), 1567–1596. doi: 10.1016/j.jcp.2007.09.017
  • Clair G., Ghidaglia J.-M., & Perlat J.-P. (2016). A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics. Journal of Computational Physics, 326, 312–333. doi: 10.1016/j.jcp.2016.08.050
  • Cockburn B., Lin S.-Y., & Shu C.-W (1989). TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems. Journal of Computational Physics, 84(1), 90–113. doi: 10.1016/0021-9991(89)90183-6
  • Cockburn B., & Shu C.-W. (1989). TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Mathematics of Computation, 52(186), 411–435.
  • De Boer A., Van der Schoot M. S., & Hester Bijl (2007). Mesh deformation based on radial basis function interpolation. Computers & Structures, 85(11–14), 784–795. doi: 10.1016/j.compstruc.2007.01.013
  • Deng X., Xie B., & Xiao F. (2017). A finite volume multi-moment method with boundary variation diminishing principle for Euler equation on three-dimensional hybrid unstructured grids. Computers & Fluids, 153, 85–101. doi: 10.1016/j.compfluid.2017.05.007
  • Donea J., Giuliani S., & Halleux J.-P. (1982). An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering, 33(1–3), 689–723. doi: 10.1016/0045-7825(82)90128-1
  • Donea J., Huerta A., Ponthot J.-Ph., & Rodríguez-Ferran A. (2004). Encyclopedia of computational mechanics Vol. 1: Fundamentals. Chapter 14: Arbitrary Lagrangian-Eulerian Methods.
  • Duarte F., Gormaz R., & Natesan S (2004). Arbitrary Lagran-gian Eulerian method for NavierStokes equations with moving boundaries. Computer Methods in Applied Mechanics and Engineering, 193(45–47), 4819–4836. doi: 10.1016/j.cma.2004.05.003
  • Dukowicz J. K., & Meltz B. JA. (1992). Vorticity errors in multidimensional Lagrangian codes. Journal of Computational Physics, 99(1), 115–134. doi: 10.1016/0021-9991(92)90280-C
  • Dumbser M., Peshkov L., Romenski E., & Zanotti Z. (2016). High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids. Journal of Computational Physics, 314, 824–862. doi: 10.1016/j.jcp.2016.02.015
  • Dumbser M., Uuriintsetseg A., & Zanotti A. (2013). On arbitrary-Lagrangian-Eulerian one-step WENO schemes for stiff hyperbolic balance laws. Communications in Computational Physics, 14(2), 301–327. doi: 10.4208/cicp.310112.120912a
  • Estruch O., Lehmkuhl O., Borrell R., Pérez Segarra C. D., & Oliva A. (2013). A parallel radial basis function interpolation method for unstructured dynamic meshes. Computers and Fluids, 80, 44–54. doi: 10.1016/j.compfluid.2012.06.015
  • Harten A., Engquist B., Osher S., & Chakravarthy S. R. (1987). Uniformly high order accurate essentially non-oscillatory schemes, III Upwind and high-resolution schemes (pp. 218–290). Berlin: Springer.
  • Harten A., Lax P. D., & van Leer B. (1983). On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1), 35–61. doi: 10.1137/1025002
  • Herman C., Jiun-Shyan C., & Ted B. (1988). Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua. Computer Methods in Applied Mechanics and Engineering, 68(3), 259–310. doi: 10.1016/0045-7825(88)90011-4
  • Hirt C. W., Amsden A. A., & Cook J. L. (1974). An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics, 14(3), 227–253. doi: 10.1016/0021-9991(74)90051-5
  • Koopmann G. H. (1967). The vortex wakes of vibrating cylinders at low Reynolds numbers. Journal of Fluid Mechanics, 28(3), 501–512. doi: 10.1017/S0022112067002253
  • Lhner, R. (2008). Applied computational fluid dynamics techniques: An introduction based on finite element methods. Fairfax, Virginia: John Wiley & Sons.
  • Lomtev I., Kirby R. M., & Karniadakis G. E. (1999). A discontinuous Galerkin ALE method for compressible viscous flows in moving domains. Journal of Computational Physics, 155(1), 128–159. doi: 10.1006/jcph.1999.6331
  • Luo H., Baum J. D., & Löhner R. (2004). On the computation of multi-material flows using ALE formulation. Journal of Computational Physics, 194(1), 304–328. doi: 10.1016/j.jcp.2003.09.026
  • Maire P.-H. (2009). A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. Journal of Computational Physics, 228(7), 2391–2425. doi: 10.1016/j.jcp.2008.12.007
  • Maire P.-H., Loubére R., & Vchal P. (2011). Staggered Lagrangian discretization based on cell-centered Riemann solver and associated hydrodynamics scheme. Communications in Computational Physics, 10(4), 940–978. doi: 10.4208/cicp.170310.251110a
  • Mavriplis D. J., & Nastase C. R. (2011). On the geometric conservation law for high-order discontinuous Galerkin discretizations on dynamically deforming meshes. Journal of Computational Physics, 230(11), 4285–4300. doi: 10.1016/j.jcp.2011.01.022
  • Mavriplis D. J., & Yang Z. (2006). Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes. Journal of Computational Physics, 213(2), 557–573. doi: 10.1016/j.jcp.2005.08.018
  • Mou B., He B.-J., Zhao D.-X., & Chau K.-w. (2017). Numerical simulation of the effects of building dimensional variation on wind pressure distribution. Engineering Applications of Computational Fluid Mechanics, 11(1), 293–309. doi: 10.1080/19942060.2017.1281845
  • Müller B. (2008). High order numerical simulation of aeolian tones. Computers & Fluids, 37(4), 450–462. doi: 10.1016/j.compfluid.2007.02.008
  • Nguyen V.-T. (2010). An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for simulations of flows over variable geometries. Journal of Fluids and Structures, 26(2), 312–329. doi: 10.1016/j.jfluidstructs.2009.11.002
  • Norberg C. (2003). Fluctuating lift on a circular cylinder: Review and new measurements. Journal of Fluids and Structures, 17(1), 57–96. doi: 10.1016/S0889-9746(02)00099-3
  • Park J. S., Yoon S.-H., & Kim C. (2010). Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids. Journal of Computational Physics, 229(3), 788–812. doi: 10.1016/j.jcp.2009.10.011
  • Persson P.-O., Bonet J., & Peraire J. (2009). Discontinuous Galerkin solution of the NavierStokes equations on deformable domains. Computer Methods in Applied Mechanics and Engineering, 198(17–20), 1585–1595. doi: 10.1016/j.cma.2009.01.012
  • Placzek A., Sigrist J.-F., & Hamdouni A. (2009). Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations. Computers & Fluids, 38(1), 80–100. doi: 10.1016/j.compfluid.2008.01.007
  • Ren X. d., Xu K., & Shyy W. (2016). A multi-dimensional high-order DG-ALE method based on gas-kinetic theory with application to oscillating bodies. Journal of Computational Physics, 316, 700–720. doi: 10.1016/j.jcp.2016.04.028
  • Roe P. L. (1981). Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2), 357–372. doi: 10.1016/0021-9991(81)90128-5
  • Rusanov V. V. (1962). Calculation of interaction of non-steady shock waves with obstacles. NRC, Division of Mechanical Engineering.
  • Shu C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Advanced numerical approximation of nonlinear hyperbolic equations (pp. 325–432). Berlin: Springer.
  • Thomas P. D., & Lombard C. K. (1979). Geometric conservation law and its application to flow computations on moving grids. AIAA Journal, 17(10), 1030–1037. doi: 10.2514/3.61273
  • Toro, E. F. (2013). Riemann solvers and numerical methods for fluid dynamics: A practical introduction. Trento: Springer Science & Business Media.
  • van der Vegt J. J. W., & Van der Ven H. (2002). Spacetime discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I general formulation. Journal of Computational Physics, 182(2), 546–585. doi: 10.1006/jcph.2002.7185
  • Vilar F., Maire P.-H., & Abgrall R. (2014). A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids. Journal of Computational Physics, 276, 188–234. doi: 10.1016/j.jcp.2014.07.030
  • Wang Z. J. (2002). Spectral (finite) volume method for conservation laws on unstructured grids basic formulation: Basic formulation. Journal of Computational Physics, 178(1), 210–251. doi: 10.1006/jcph.2002.7041
  • Wang Z. J., & Liu Y. (2002). Spectral (finite) volume method for conservation laws on unstructured grids: II Extension to two-dimensional scalar equation. Journal of Computational Physics, 179(2), 665–697. doi: 10.1006/jcph.2002.7082
  • Woodward P., & Colella P. (1984). The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 54(1), 115–173. doi: 10.1016/0021-9991(84)90142-6
  • Xiao F., Akoh R., & Ii S. (2006). Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows. Journal of Computational Physics, 213(1), 31–56. doi: 10.1016/j.jcp.2005.08.002
  • Xie B., Deng X., Sun Z. Y., & Xiao F. (2017). A hybrid pressure-density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method. Journal of Computational Physics, 335, 637–663. doi: 10.1016/j.jcp.2017.01.043
  • Xie B., Ii S., Ikebata A., & Xiao F. (2014). A multi-moment finite volume method for incompressible Navier Stokes equations on unstructured grids: Volume-average/point-value formulation. Journal of Computational Physics, 277, 138–162. doi: 10.1016/j.jcp.2014.08.011
  • Xie B., & Xiao F. (2014). Two and three dimensional multi-moment finite volume solver for incompressible Navier–Stokes equations on unstructured grids with arbitrary quadrilateral and hexahedral elements. Computers & Fluids, 104, 40–54. doi: 10.1016/j.compfluid.2014.08.002
  • Xie B., & Xiao F. (2016). A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows. Journal of Computational Physics, 327, 747–778. doi: 10.1016/j.jcp.2016.09.054
  • Zhang L. P., Liu W., Li M., He X., & Zhang H. X. (2014). A class of DG/FV hybrid schemes for conservation law IV: 2D viscous flows and implicit algorithm for steady cases. Computers & Fluids, 97, 110–125. doi: 10.1016/j.compfluid.2014.04.002