The nonlinear modified equation approach to analyzing finite difference schemesThe nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.
Document ID
19810053153
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Klopfer, G. H. (Nielsen Engineering and Research, Inc. Mountain View, Calif., United States)
Mcrae, D. S. (NASA Ames Research Center Moffett Field, Calif.; USAF, Flight Vehicle Technology Office, Wright-Patterson AFB, Ohio, United States)