A weak statement perturbation CFD algorithm with high-order phase accuracy for hyperbolic problems
Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can...
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| Published in | Computer methods in applied mechanics and engineering Vol. 131; no. 3; pp. 209 - 232 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
1996
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 |
| DOI | 10.1016/0045-7825(95)00863-2 |
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| Abstract | Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to high order. The procedure is analyzed via a von Neumann frequency analysis, and verification CFD solutions are reported in one and two dimensions. Finally, using the element specific (local) Courant number, a
continuum (total) time integration procedure is derived that can directly produce a final time solution
independent of mesh measure. |
|---|---|
| AbstractList | Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to high order. The procedure is analyzed via a von Neumann frequency analysis, and verification CFD solutions are reported in one and two dimensions. Finally, using the element specific (local) Courant number, a
continuum (total) time integration procedure is derived that can directly produce a final time solution
independent of mesh measure. Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to high order. The procedure is analyzed via a von Neumann frequency analysis, and verification CFD solutions are reported in one and two dimensions. Finally, using the element specific (local) Courant number, a continuum (total) time integration procedure is derived that can directly produce a final time solution independent of mesh measure. |
| Author | Baker, A.J. Roy, Subrata |
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| Keywords | Finite element method Perturbation method Wave propagation Modal analysis Flow(fluid) Fluid-structure interactions Fourier analysis Taylor series Galerkin method Numerical method |
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| References | S.B. Mulay, Private communications, 1993. Vichenevetsy, Bowles (BIB12) 1982 Hirsch (BIB7) 1992 Baker (BIB1) 1983 Baker, Williams, Chaffin, Roy (BIB4) 1993; Vol. 1 Baker, Pepper (BIB2) 1991 Baker, Kim (BIB3) 1987; 7 Kreiss, Lorenz (BIB8) 1989 Haras, Ta'asan (BIB6) 1993 Lele (BIB10) 1992; 103 Demkowicz, Oden, Rachowicz, Hardy (BIB5) 1989; 77 Lax (BIB9) 1954; 7 Lele (10.1016/0045-7825(95)00863-2_BIB10) 1992; 103 Baker (10.1016/0045-7825(95)00863-2_BIB1) 1983 Baker (10.1016/0045-7825(95)00863-2_BIB3) 1987; 7 Kreiss (10.1016/0045-7825(95)00863-2_BIB8) 1989 Baker (10.1016/0045-7825(95)00863-2_BIB4) 1993; Vol. 1 10.1016/0045-7825(95)00863-2_BIB11 Demkowicz (10.1016/0045-7825(95)00863-2_BIB5) 1989; 77 Hirsch (10.1016/0045-7825(95)00863-2_BIB7) 1992 Haras (10.1016/0045-7825(95)00863-2_BIB6) 1993 Vichenevetsy (10.1016/0045-7825(95)00863-2_BIB12) 1982 Baker (10.1016/0045-7825(95)00863-2_BIB2) 1991 Lax (10.1016/0045-7825(95)00863-2_BIB9) 1954; 7 |
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| Title | A weak statement perturbation CFD algorithm with high-order phase accuracy for hyperbolic problems |
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