A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes

Abstract We propose a formulation of the three-dimensional Navier–Stokes equations, which expresses the inviscid part of the equations as a decomposition into several plane waves which are aligned with the numerical grid. The resulting equations are very well suited to numerical solution using compact high order upwind schemes. Boundary conditions and blockwise decomposition of the computational domain are particularly straightforward. Such advantages make the formulation attractive, even when using central or pseudospectral differencing methods. Numerical examples are presented.

[1]  L. Zannetti,et al.  Some Tests on Finite Difference Algorithms for Computing Boundaries in Hyperbolic Flows , 1978 .

[2]  R. Courant,et al.  On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .

[3]  D. S. Butler.  The numerical solution of hyperbolic systems of partial differential equations in three independent variables , 1960, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  L. Zannetti,et al.  About the numerical modelling of multidimensional unsteady compressible flow , 1989 .

[5]  John Van Rosendale,et al.  Upwind and high-resolution schemes , 1997 .

[6]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[7]  A I Tolstykh.  High Accuracy Non-Centered Compact Difference Schemes for Fluid Dynamics Applications , 1994 .

[8]  G. Colasurdo,et al.  Unsteady compressible flow - A computational method consistent with the physical phenomena , 1981 .

[9]  Robert D. Moser,et al.  A numerical study of turbulent supersonic isothermal-wall channel flow , 1995, Journal of Fluid Mechanics.

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

[11]  C. Hirsch,et al.  Characteristic decomposition methods for the multidimensional euler equations , 1986 .

[12]  Gino Moretti,et al.  The λ-scheme , 1979 .

[13]  R. Friedrich,et al.  Direct Numerical Simulation of Turbulent Compressible and Incompressible Wall-Bounded Shear Flows , 1999 .

[14]  Philip L. Roe,et al.  Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics , 1986 .

[15]  Nikolaus A. Adams,et al.  A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems , 1996 .

[16]  Gino Moretti,et al.  A technique for integrating two-dimensional Euler equations , 1987 .

[17]  M. Lighthill,et al.  Waves In Fluids , 2002 .

[18]  S. Chakravarthy,et al.  The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations , 1980 .

[19]  Gino Moretti,et al.  COMPUTATION OF FLOWS WITH SHOCKS , 1987 .

[20]  Gordon Erlebacher,et al.  Nonlinear Strong Shock Interactions: A Shock-Fitted Approach , 1998 .

[21]  Markus J. Kloker,et al.  A Robust High-Resolution Split-Type Compact FD Scheme for Spatial Direct Numerical Simulation of Boundary-Layer Transition , 1997 .

[22]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[23]  G. Moretti,et al.  Comparison of different integration schemes based on the concept of characteristics as applied to the ablated blunt body problem , 1982 .

[24]  C. Kentzer.  Physics and computations of gas dynamic waves , 1989 .

[25]  B. Riemann.  über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite , 1860 .

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