An Alternating Direction Implicit Method for Modeling of Fluid Flow

An Alternating-Direction-Implicit Algorithm for Unsteady Potential Flow

An implicit finite-difference scheme is presented for the efficient computation of unsteady potential flow about airfoils. The formulation uses density and the velocity potential a s dependent variables and is cast in conservation form to a s s u r e the theoretically c o r r ~ c t determination of shockwave location and speed. TO enable houndary conditions to b e imposed directly on the airfoi...

A parallel alternating direction implicit preconditioning method *

Jiang, H. and Y.S. Wong, A parallel alternating direction implicit preconditioning method, Journal of Computational and Applied Mathematics 36 (1991) 209-226. The alternating direction implicit (ADI) iterative method is an efficient iterative method to solve systems of linear equations due to its extremely fast convergence. The AD1 method has also been used successfully as a preconditioner in s...

An Alternating Direction Method

combination of a's yields the numerical coefficient for that combination. For example, in the summation for Su given in Table 2, 1/ao4 has as the ai*-1aB_*+i coefficient ai3a8 which, in turn, has the numerical coefficient 11. The ai2a3a6 combination has 2 ! X 1 ! X 1 ! as the product of the factorials of the exponents. If 11 X 3 ! X 1 ! is divided by 2 ! X 1 ! X 1 !, the result is 33 which is t...

Implicit Alternating Direction Methods

in general plane regions and with respect to linear boundary conditions, is a classical problem of numerical analysis. Many such boundary value problems have been solved successfully on high-speed computing machines, using the (iterative) Young-Frankel "successive overrelaxation" (SOR) method as defined in [l] and [2], and variants thereof ("line" and "block" overrelaxation). For this method, e...

A Note on the Alternating Direction Implicit Method for the Numerical Solution of Heat Flow Problems

1. Introduction. In companion papers [l; 6] recently Peaceman, Rachford, and the author introduced a finite difference technique called therein the alternating direction implicit method for approximating the solution of transient and permanent heat flow problems in two space variables. The validity of the method was established only in the case of a rectangular domain. Since then the procedure ...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method