Spurious waves in discrete computation of wave phenomena and flow problems

[1]  L. Kovasznay,et al.  Non-linear interactions in a viscous heat-conducting compressible gas , 1958, Journal of Fluid Mechanics.

[2]  James Lighthill,et al.  Waves In Fluids , 1966 .

[3]  Heinz-Otto Kreiss,et al.  Methods for the approximate solution of time dependent problems , 1973 .

[4]  J. E. Dendy Two Methods of Galerkin Type Achieving Optimum $L^2 $ Rates of Convergence for First Order Hyperbolics , 1974 .

[5]  M. J. P. Cullen,et al.  A Finite Element Method for a Non-linear Initial Value Problem , 1974 .

[6]  Burton Wendroff,et al.  The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines , 1974 .

[7]  L. Wahlbin,et al.  A modified Galerkin procedure with Hermite cubics for hyperbolic problems , 1975 .

[8]  H. Schönheinz G. Strang / G. J. Fix, An Analysis of the Finite Element Method. (Series in Automatic Computation. XIV + 306 S. m. Fig. Englewood Clifs, N. J. 1973. Prentice‐Hall, Inc. , 1975 .

[9]  William H. Raymond,et al.  Selective Damping in a Galerkin Method for Solving Wave Problems with Variable Grids , 1976 .

[10]  Richard Grotjahn,et al.  Some Inaccuracies in Finite Differencing Hyperbolic Equations , 1976 .

[11]  S. Orszag,et al.  Numerical solution of problems in unbounded regions: Coordinate transforms , 1977 .

[12]  Robert Vichnevetsky,et al.  Advances in computer methods for partial differential equations II : proceedings of the second IMACS (AICA) International Symposium on Computer Methods for Partial Differential Equations, held at Lehigh University, Bethlehem, Pennsylvania, U.S.A., June 22-24, 1977 , 1977 .

[13]  J. Pedlosky Geophysical Fluid Dynamics , 1979 .

[14]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[15]  J. Baum,et al.  Numerical techniques for solving nonlinear instability problems in solid rocket motors , 1981 .

[16]  Robert Vichnevetsky,et al.  Propagation through numerical mesh refinement for hyperbolic equations , 1981 .

[17]  L. Trefethen Group velocity in finite difference schemes , 1981 .

[18]  Robert Vichnevetsky The energy flow equation , 1984 .

[19]  Robert Vichnevetsky,et al.  High order numerical sommerfeld boundary conditions: Theory and experiments , 1985 .

[20]  R. Vichnevetsky,et al.  ADVANCES IN COMPUTER METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS - VI Proceedings ofthe Sixth IMACS International Symposium on Computer Methods for Partial Differential Equations , 1987 .

[21]  Robert Vichnevetsky,et al.  Wave propagation and reflection in irregular grids for hyperbolic equations , 1987 .

[22]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[23]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[24]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[25]  S. Lele Compact finite difference schemes with spectral-like resolution , 1992 .

[26]  Paolo Orlandi,et al.  Boundary Condition Influence on the Flow Around a Circular Cylinder , 1993 .

[27]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[28]  Shlomo Ta'asan,et al.  Finite difference schemes for long-time integration , 1994 .

[29]  M. Minion,et al.  Performance of Under-resolved Two-Dimensional Incompressible Flow , 1995 .

[30]  D. Thévenin,et al.  Accurate Boundary Conditions for Multicomponent Reactive Flows , 1995 .

[31]  P. Roache Fundamentals of computational fluid dynamics , 1998 .

[32]  Jeffrey L. Young,et al.  Practical aspects of higher-order numerical schemes for wave propagation phenomena , 1999 .

[33]  Soogab Lee,et al.  Grid-optimized dispersion-relation-preserving schemes on general geometries for computational aeroacoustics , 2001 .

[34]  J. Szmelter Incompressible flow and the finite element method , 2001 .

[35]  T. Poinsot,et al.  Theoretical and numerical combustion , 2001 .

[36]  Tapan K. Sengupta,et al.  High Accuracy Compact Schemes and Gibbs' Phenomenon , 2004, J. Sci. Comput..

[37]  Tapan K. Sengupta,et al.  Analysis of central and upwind compact schemes , 2003 .

[38]  Emmanuel Hanert,et al.  On some spurious mode issues in shallow-water models using a linear algebra approach , 2005 .

[39]  Ru-Xun Liu,et al.  Combined finite volume–finite element method for shallow water equations , 2005 .

[40]  Tapan K. Sengupta,et al.  Galerkin finite element methods for wave problems , 2005 .

[41]  Tapan K. Sengupta,et al.  A new flux-vector splitting compact finite volume scheme , 2005 .

[42]  Tapan K. Sengupta,et al.  High Accuracy Schemes for DNS and Acoustics , 2006, J. Sci. Comput..

[43]  Pierre Sagaut,et al.  A linear dispersive mechanism for numerical error growth: spurious caustics , 2006 .

[44]  Ch. Hirsch,et al.  Fundamentals Of Computational Fluid Dynamics , 2016 .

[45]  Shan Zhao,et al.  On the spurious solutions in the high-order finite difference methods for eigenvalue problems , 2007 .

[46]  T. K. Sengupta,et al.  Error dynamics: Beyond von Neumann analysis , 2007, J. Comput. Phys..

[47]  Tapan K. Sengupta,et al.  Design and analysis of a new filter for LES and DES , 2009 .

[48]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[49]  Tapan K. Sengupta,et al.  New explicit two-dimensional higher order filters , 2010 .

[50]  Thierry Poinsot,et al.  Instabilities of flows : with and without heat transfer and chemical reaction , 2010 .

[51]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[52]  Tapan K. Sengupta,et al.  Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods , 2011, J. Comput. Phys..