Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (4): 489-499.

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THE UPWIND OPERATOR SPLITTING FINITE DIFFERENCE METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

 YUAN Yi-Rang   

  1. (Institute of Mathematics, Shandong University, Jinan 250100, China)
  • Online:2002-10-14 Published:2002-10-14
  • Supported by:

    The project supported by the Major State Basic Research Program of China (19990328), NNSF of China (19871051, 19972039) and the Doctorate Foundation of the State Education Commission.

Abstract:

For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decompo-sition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.

Key words: Two-phase displacement, two-dimensional compressibility, upwind operator splitting, finite difference schemes, convergence analysis

CLC Number: 

  • 65M15
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