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Hybrid Methods in Engineering

ISSN Druckformat: 1099-2391
ISSN Online: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v2.i1.60
11 pages

MATHEMATICAL AND PHYSICAL ASPECTS IN CONSTRUCTING NUMERICAL SCHEMES FOR SOLVING THE ADVECTION EQUATION

ABSTRAKT

The article addresses stability limits and accuracy of methods of advancing the solution of a system of ordinary differential equations (ODEs) in time by the Runge-Kutta (RK) and Taylor series (TS) methods. This system of ODEs arises as a result of discretizing the advection equation (a partial differential equation, PDE) spatially. Symbolic manipulation is used in the stability analysis. The Von Neumann linear stability method is illustrated with the aid of symbolic programming. The program is general and can be extended easily to analyze the stability of higher-order advection and advection-diffusion schemes. It is found that the RK and TS methods produce identical results as far as accuracy and stability limit are concerned. The TS method requires less memory storage than the RK method. Also, an explicit scheme based on the physics of the problem is constructed. The scheme is unconditionally stable and accurate for all values of Courant parameter.


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