Discretization error estimation and exact solution generation using the method of nearby problems.

Sinclair, Andrew J. (Auburn University Auburn, AL) ; Raju, Anil (Auburn University Auburn, AL) ; Kurzen, Matthew J. (Virginia Tech Blacksburg, VA) ; Roy, Christopher John (Virginia Tech Blacksburg, VA) ; Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)

Sandia National Laboratories

关键词: Navier-Stokes Equations;    Numerical Solution;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Extrapolation;    Partial Differential Equations;   

DOI  :  10.2172/1029791
RP-ID  :  SAND2011-7118
RP-ID  :  AC04-94AL85000
RP-ID  :  1029791

美国|英语

来源: UNT Digital Library

【 摘 要 】

The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only requires a single additional numerical solution on the same grid (as compared to Richardson extrapolation which requires additional numerical solutions on systematically-refined grids). When used for error estimation, it was found that continuity between spline zones was not required. A number of cases were examined including 1D and 2D Burgers equation, the 2D compressible Euler equations, and the 2D incompressible Navier-Stokes equations. The discretization error estimation results compared favorably to Richardson extrapolation and had the advantage of only requiring a single grid to be generated.