Abstract
This chapter discusses the domain decomposition techniques to solve the Navier-Stokes equation. A numerical algorithm to approximately solve the problems of mathematical physics on modern parallel computers is based on domain decomposition techniques. In this chapter, domain decomposition schemes have been developed to numerically solve initial/boundary value problems for the Navier-Stokes equations in the primitive variable pressure-velocity. On the basis of the general theory of operator-splitting schemes, various classes of domain decomposition schemes for problems of convectio-diffusion are investigated. In simulation of incompressible flows, an elliptic problem for the pressure can be replaced on separate elliptic problems for the pressure in particular subdomains. Hence, it is possible to construct non-iterative region-additives for the Navier-Stokes equations. Therefore, a non-iterative region-additive scheme is constructed for the Navier-Stokes equations.
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