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Full-Text Articles in Physical Sciences and Mathematics
Boundary Approximations For Implicit Schemes For .One-Dimensional Inviscid Equations Of Gasdynamics, Helen Yee, R. M. Beam, R. F. Warming
Boundary Approximations For Implicit Schemes For .One-Dimensional Inviscid Equations Of Gasdynamics, Helen Yee, R. M. Beam, R. F. Warming
United States National Aeronautics and Space Administration: Publications
The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations is examined for initial boundary-value problems of the hyperbolic type. For the numerical experiments the one-dimensional inviscid gasdynamic equations in conservation law form are selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit vs implicit boundary schemes, and unconditionally stable schemes.
On The Application And Extension Of Harten's High-Resolution Scheme, Helen C. Yee, R. F. Warming, Amiran Harten
On The Application And Extension Of Harten's High-Resolution Scheme, Helen C. Yee, R. F. Warming, Amiran Harten
United States National Aeronautics and Space Administration: Publications
Xost first-order upstream conservative differencing methods can capture shocks quite well for one-dimensional problems. A direct application of these first-order methods to two-dimensional problems does not necessarily produce the same type of accuracy unless the shocks are locally aligned with the mesh. Harten has recently developed a second-order high-resolution explicit method for the numerical computation of weak solutions of one-dimensional hyperbolic conservation laws. The main objectives of this paper are (a) to examine the shock resolution of Harten's method for a two-dimensional shock reflection problem, (b) to study the use of a high-resolution scheme as a post-processor to an approximate …