an:04027077
Zbl 0631.76087
Yee, H. C.; Warming, R. F.; Harten, A.
Implicit total variation diminishing (TVD) schemes for steady-state calculations
EN
J. Comput. Phys. 57, 327-360 (1985).
00149794
1985
j
76N15 76L05 76M99
implicit unconditionally stable high-resolution TVD scheme; steady-state calculations; explicit and implicit second-order accurate schemes; weak solutions of one-dimensional hyperbolic conservation laws; spurious oscillations; rapid convergence; highly resolved approximation to the steady-state solution; two-dimensional compressible inviscid equations of gas dynamics; two-dimensional fluid flows
The application of a new implicit unconditionally stable high-resolution TVD scheme to steady-state calculations is examined. It is a member of a one-parameter family of explicit and implicit second-order accurate schemes developed by the third author [ibid. 49, 357-393 (1983; Zbl 0565.65050)] for the computation of weak solutions of one-dimensional hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a fairly rapid convergence rate, but also generates a highly resolved approximation to the steady-state solution. A detailed implementation of the implicit scheme for the one- and two-dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one- and two-dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.
Zbl 0565.65050