Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this article, a stream function-velocity formulation of the two-dimensional steady-state Navier-Stokes equations representing incompressible fluid flows in 2D domains is proposed.
132 citations
TL;DR: This work has developed several finite difference algorithms for the solution of the problem in its most general formulation (i.e. for any set of single-cell physiological state functions) and verified the validity of the developed algorithms.
132 citations
TL;DR: In this paper, the use of the artificial compression method for the computation of discontinuous solutions of a single conservation law by finite difference methods is discussed, and the numerical implementation of artificial compression is described.
Abstract: The paper discusses the use of the artificial compression method for the computation of discontinuous solutions of a single conservation law by finite difference methods. The single conservation law has either a shock or a contact discontinuity. Any monotone finite difference scheme applied to the original equation smears the discontinuity, while the same scheme applied to the equation modified by an artificial compression flux produces steady progressing profiles. If L is any finite difference scheme in conservation form and C is an artificial compressor, the split flux artificial compression method CL is a corrective scheme: L smears the discontinuity while propagating it; C compresses the smeared transition toward a sharp discontinuity. Numerical implementation of artificial compression is described.
132 citations
TL;DR: In this article, a general, implicit, numerical, marching procedure is presented for the solution of parabolic partial differential equations, with special reference to those of the boundary layer, where the main novelty lies in the choice of a grid which adjusts its width so as to conform to the thickness of the layer in which significant property gradients are present.
132 citations
TL;DR: In this article, a computationally simple, numerical algorithm capable of solving a wide variety of two-dimensional, variably saturated flow problems is developed, which avoids mass-balance errors in unsaturated regions and is numerically stable.
132 citations