A novel stabilization method for high-order shock fitting with finite element methods

[1]  Andrew Corrigan,et al.  A moving discontinuous Galerkin finite element method for flows with interfaces , 2018, International Journal for Numerical Methods in Fluids.

[2]  V. Venkatakrishnan,et al.  IMPLICIT METHOD FOR THE COMPUTATION OF UNSTEADY FLOWS ON UNSTRUCTURED GRIDS , 1995 .

[3]  George Em Karniadakis,et al.  A triangular spectral element method; applications to the incompressible Navier-Stokes equations , 1995 .

[4]  Renato Paciorri,et al.  An unstructured, three-dimensional, shock-fitting solver for hypersonic flows , 2013 .

[5]  Timothy J. Baker,et al.  Mesh Movement and Metamorphosis , 2002, Engineering with Computers.

[6]  F. Marconi,et al.  Computation of Three Dimentional Flows about aircraft configurations , 1973 .

[7]  Brian T. Helenbrook,et al.  High-Order Shock Fitting with Finite Element Methods , 2020 .

[8]  George Em Karniadakis,et al.  TetrahedralhpFinite Elements , 1996 .

[9]  Mirco Ciallella,et al.  Extrapolated Shock Tracking: Bridging shock-fitting and embedded boundary methods , 2020, J. Comput. Phys..

[10]  S. Rebay,et al.  High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations , 1997 .

[11]  Per-Olof Persson,et al.  An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions , 2017, J. Comput. Phys..

[12]  Brian T. Helenbrook,et al.  Preconditioning for dual-time-stepping simulations of the shallow water equations including Coriolis and bed friction effects , 2008, J. Comput. Phys..

[13]  James J. Quirk,et al.  A Contribution to the Great Riemann Solver Debate , 1994 .

[14]  Renato Paciorri,et al.  Unsteady shock‐fitting for unstructured grids , 2016 .

[15]  Chi-Wang Shu,et al.  Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: Triangular elements , 2019, J. Comput. Phys..

[16]  B. Helenbrook,et al.  High-order adaptive arbitrary-Lagrangian–Eulerian (ALE) simulations of solidification , 2018 .

[17]  Jean-Marc Moschetta,et al.  Shock wave numerical structure and the carbuncle phenomenon , 2005 .

[18]  Renato Paciorri,et al.  A shock-fitting technique for 2D unstructured grids , 2009 .

[19]  Keiichi Kitamura,et al.  Evaluation of Euler Fluxes for Hypersonic Flow Computations , 2009 .

[20]  G. Moretti,et al.  A time-dependent computational method for blunt body flows. , 1966 .

[21]  Jun Liu,et al.  A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes , 2017, J. Comput. Phys..

[22]  Alireza Mazaheri,et al.  Efficient high-order discontinuous Galerkin schemes with first-order hyperbolic advection-diffusion system approach , 2016, J. Comput. Phys..

[23]  Ian T. Cameron,et al.  A four-stage index 2 diagonally implicit Runge-Kutta method , 2002 .

[24]  Brian T. Helenbrook,et al.  Mesh deformation using the biharmonic operator , 2003 .

[25]  Michael J. Brazell,et al.  p=2 Continuous finite elements on tetrahedra with local mass matrix inversion to solve the preconditioned compressible Navier–Stokes equations , 2013 .

[26]  Pradeep Singh Rawat,et al.  On high-order shock-fitting and front-tracking schemes for numerical simulation of shock-disturbance interactions , 2010, J. Comput. Phys..

[27]  Timothy J. Baker Mesh deformation and modification for time dependent problems , 2003 .

[28]  Brian T. Helenbrook,et al.  A two-fluid spectral-element method , 2001 .

[29]  Renato Paciorri,et al.  Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique , 2011, J. Comput. Phys..

[30]  Mikhail S. Ivanov,et al.  Computation of weak steady shock reflections by means of an unstructured shock-fitting solver , 2010 .

[31]  Jean-Marc Moschetta,et al.  Robustness versus accuracy in shock-wave computations , 2000 .

[32]  M. D. Salas,et al.  Spectral methods for the Euler equations. II - Chebyshev methods and shock fitting , 1985 .

[33]  Moshe Dubiner Spectral methods on triangles and other domains , 1991 .