Algorithms for the exact solution of two matrix equations occurring in the driven cavity problem

• Autorzy: Klonowska M. E. , Prosnak W. J.
• Języki publikacji: EN

Abstrakty

EN

It is shown that two particular systems of linear equations, derived in an earlier paper by Prosnak and Kosma (1991), can be solved in an exact time- and storage-saving manner. First of all, by the proper elimination of unknowns, each system can be reduced to a smaller one containing only half of the unknowns. In the first case, the matrix of coefficients of the so reduced system turns out to be tridiagonal, its elements consisting of square submatrices. Moreover, the reduced system can be split into two independent ones. In the second case, the matrix of the reduced system can be presented as the product of two triangular ones, each one being partitioned in square submatrices. Corresponding algorithms and computer programs have been developed in order to investigate whether some economy in storage and computing time is really attainable. Affirmative conclusions are drawn from the results of computations. This means that the new method of solving problems governed by the Navier-Stokes equations, presented in the cited paper, can be applied in a more effective manner.

Słowa kluczowe

EN

Navier-Stokes equations; elimination of pressure; driven cavity problem; improvement of the process of solution

• Wydawca: Polish Academy of Sciences, Institute of Oceanology ; Elsevier
• Czasopismo: Oceanologia
• Rocznik: 1999
• Tom: No. 41 (1)
• Strony: 3--23
• Opis fizyczny: Bibliogr. 5 poz., tab., wykr.

Twórcy

autor

Klonowska M. E.

autor

Prosnak W. J.

• Institute of Oceanology, Polish Academy of Sciences, Powstańców Warszawy 55, 81–712 Sopot, Poland,

Bibliografia

• 1. Klonowska M. E., Kołodziejczyk M., Tests of a new method for the numerical solution of the Navier-Stokes equations. Part I: plane unsteady flow in finite, rectangular domains, Appl. Mech. Eng., (in press).
• 2. Lambert J. D., 1973, Computational methods in ordinary differential equations, John Wiley & Sons, London–New York–Sydney, 278 pp.
• 3. Prosnak W. J., 1993, Introduction to numerical fluid mechanics. Part A: fundamental numerical methods, Ossolineum, Wrocław, 490 pp., (in Polish).
• 4. Prosnak W. J., Kosma Z. J., 1991, On a new method for the numerical solution of the Navier-Stokes equations, Acta Mech., 89, 45-63.
• 5. Zurmühl R., 1949, Zur numerischen Aufl¨osung linearer Gleichungssysteme nach dem Matrizenverfahren von Banachiewicz, Z. angew. Math. Mech., 23, 76-84.