Stability analysis of intermediate boundary conditions in approximate factorization schemes

The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. We show that the treatment suggested by Holst led to a restriction on the time step and suggest ways to overcome this restriction. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the Von Neumann method.

[1]  A. Jameson,et al.  Implicit Approximate-Factorization Schemes for Steady Transonic Flow Problems , 1978 .

[2]  H. Kreiss,et al.  Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II , 1972 .

[3]  R. F. Warming,et al.  An Implicit Factored Scheme for the Compressible Navier-Stokes Equations , 1977 .

[4]  T. Holst,et al.  An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh , 1978 .

[5]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[6]  Eli Turkel,et al.  Boundary conditions for multistep finite-difference methods for time-dependent equations☆ , 1978 .

[7]  F. Thames,et al.  Accuracy and stability of time-split finite-difference schemes , 1981 .

[8]  Systems of difference equations with general homogeneous boundary conditions , 1969 .

[9]  Antony Jameson,et al.  Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method , 1979 .

[10]  A. Jameson,et al.  Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems , 1977 .

[11]  J. Trapp,et al.  A simple heuristic method for analyzing the effect of boundary conditions on numerical stability , 1976 .

[12]  A. Jameson.  Iterative solution of transonic flows over airfoils and wings, including flows at mach 1 , 1974 .

[13]  E. Tadmor,et al.  Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II , 1978 .

[14]  W. F. Ballhaus,et al.  Implicit approximate-factorization schemes for the low-frequency transonic equation , 1975 .

[15]  T. Holst.  Implicit Algorithm for the Conservative Transonic Full-Potential Equation Using an Arbitrary Mesh , 1979 .

[16]  Scott D. Thomas,et al.  Numerical solution of transonic wing flowfields , 1982 .

[17]  W. R. Briley,et al.  Solution of the three-dimensional compressible Navier-Stokes equations by an implicit technique , 1975 .