[求助]流体力学知识！

delayan2000

请问那位能给我解释一下MAC方法？

sillybear

It is well known that the marker and cell method (MAC) is one of the simplest
and most eective numerical schemes for solving Stokes equations and Navier{Stokes
equations. The MAC scheme was introduced by V. I. Lebedev [9] and B. J. Daly et
al. [5] in the middle of sixties and has been widely used in engineering applications.
The MAC method is outside of the framework of the nite element method and
is characterized by the following fact: the MAC method decomposes the uid into
squares or rectangular cells and discretizes the pressure at the center of the cell.
Furthermore, it discretizes the rst component of the velocity at the midpoint of the
vertical sides of the cells and the second component at the midpoint of the horizontal
sides of the cells. It does not discretize the two components of the velocity at the
same points. S. Choudhury and R. A. Nicolaides [3], R. A. Nicolaides [10], and R. A.
Nicolaides and X. Wu [11] analyze the MAC method and the related method based
on the covolume method framework. In the paper [6] by V. Girault and H. Lopez
the MAC method is interpreted as a mixed nite element method of the \velocity-
vorticity" variational formulation of the Navier{Stokes equations coupled with the
quadrature formula. Moreover, the error estimates for the MAC scheme are given.
In this paper we nd the natural connection between the MAC scheme and the new
mixed nite element scheme of the variational formulation with primitive variables of the Stokes equations. Furthermore, the optimal error estimates for the MAC scheme
are obtained. The natural connection brings many advantages, such as setting the
framework of the nite element method for the MAC scheme, so many mathematical
tools are available to analyze the MAC scheme. In fact, this connection is a bridge
for extending the MAC scheme to high-order approximations and three-dimensional
cases.
[9][9] V.L. LEBEDEV, Dierence analogues of orthogonal decompositions, fundamental dierential
operators and certain boundary-value problems of mathematical physics, Z. Vycisl. Mat. i
Mat. Fiz., 4 (1964), pp. 449{465 (in Russian).
[5] B.J. DALY, F.H. HARLOW, J.P. SHANNON, AND J.E. WELCH, The MAC Method, Tech. report
LA-3425, Los Alamos Scientic Laboratory, University of California, 1965.

sillybear

[3] S. CHOUDHURY AND R.A. NICOLAIDES, Discretization of incompressible vorticity-velocity
equations on triangular meshes, Internat. J. Numer. Methods Fluids, 11 (1990), pp. 823{
833.
[10] R.A. NICOLAIDES, Analysis and convergence of the MAC scheme. The linear problem, SIAM
J. Numer. Anal., 29 (1992), pp. 1579{1591.
[11] R.A. NICOLAIDES AND X. WU, Analysis and convergence of the MAC scheme. Navier-Stokes
equations, Math. Comp., 65 (1996), pp. 29{44.
[6] V. GIRAULT AND H. LOPEZ, Finite element error estimates for the MAC scheme, IMA J.
Numer. Anal., 16 (1996), pp. 347{379.

licongzhang

请问那位能帮我解释一下simple方法？

dql

simple有很多种演变了simpler,simplec等.你可以参考:
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