×

zbMATH — the first resource for mathematics

High order finite difference schemes with application to wave propagation problems. (English) Zbl 1165.65383
From the abstract: We consider the approximate solution to wave propagation problems by a family of fully discrete finite difference implicit schemes. The stability of mixed initial boundary problems is investigated. A wide series of computational experiments is performed.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] M.A. Pirozzi , High-accuracy finite difference methods for systems of conservation laws. I , Technical Report, Istituto di Matematica , Istituto Universitario Navale , Marzo 1999 .
[2] M.A. Pirozzi , A class of semi-implicit schemes for wave propagation problems , Annali dell’Istituto Universitario Navale , vol. LXIII ( 1997 ), pp. 7 - 10 .
[3] M.A. Pirozzi , Numerical simulation of fluid dynamic problems on distributed memory parallel computers , Concurrency: Practice and Experience, vol. 9 ( 1997 ), pp. 989 - 998 . Zbl 0895.76059 · Zbl 0895.76059
[4] M.A. Pirozzi , On boundary conditions for the numerical solution of fluid dynamic problems , Calcolo , 26 ( 10 ) ( 1989 ), pp. 149 - 165 . MR 1083051 | Zbl 0708.76045 · Zbl 0708.76045 · doi:10.1007/BF02575726
[5] M.A. Pirozzi , Sulla stabilit√† di condizioni all’interfaccia nel raffinamento dei reticoli , Atti del Convegno Nazionale di Analisi Numerica , 1989 , pp. 413 - 422 .
[6] A. Lerat - Z. N. WU, Stable conservative multidomain treatments for implicit Euler solvers , J. Comput. Phys. , 123 ( 1996 ), pp. 45 - 64 . MR 1370375 | Zbl 0839.76065 · Zbl 0839.76065 · doi:10.1006/jcph.1996.0004
[7] C.A.J. Fletcher , Computational techniques for fluid dynamics 1 , Springer Verlag , 1991 . MR 1104657 | Zbl 0717.76001 · Zbl 0717.76001
[8] G.A. Sod , Numerical methods in fluid dynamics , Cambridge University Press , 1989 . MR 832441 | Zbl 0592.76001 · Zbl 0592.76001 · doi:10.1017/CBO9780511753138
[9] R.D. Richtmyer - K. W. MORTON, Difference methods for initial-value problems, 2nd eds ., J. Wiley , 1967 . MR 220455 | Zbl 0155.47502 · Zbl 0155.47502
[10] D.R. Emerson et al., Parallel computational fluid dynamics , Elsevier Science B. V. , 1998 . MR 1634267 · Zbl 0895.68148
[11] A. Quarteroni - A. Valli , Numerical approximation of partial differential equations , Springer Verlag , 1994 . MR 1299729 | Zbl 0803.65088 · Zbl 0803.65088
[12] C.A.J. Fletcher , Computational techniques for fluid dynamics 2 , Springer Verlag , 1991 . MR 1122807 | Zbl 0717.76001 · Zbl 0717.76001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.