Fast non-symmetric iterations and efficient preconditioning for Navier-Stokes equations

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:219597

Silvester, D ^[1]; Elman, H ^[2]

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1. UMIST, Manchester (United Kingdom)
2. Univ. of Maryland, College Park, MD (United States)

Discretisation of the steady-state Navier-Stokes equations: (u.grad)u-{nu}{del}{sup 2}u + grad p = 0; div u = 0 [1]. in some flow domain {Omega} {contained_in} IR{sup d}, (d = 2 or 3), gives a system of non-linear algebraic equations for discretised variables u (the velocity), and p (the pressure). The authors assume that appropriate boundary conditions are imposed. The non-linear equation system can be linearised using a fixed-point (Picard) iteration to give a matrix system which must be solved at every iteration. Part of this matrix is block diagonal, and consists of d convection-diffusion operators, one for each component of velocity. Two difficulties arise when solving this matrix equation. Firstly, the block diagonal part is not symmetric, although under certain conditions the symmetric part is positive definite. Secondly, the overall system is indefinite. This makes the design of fast and efficient iterative solvers for discretised Navier-Stokes operators an extremely challenging task.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 219597
• Report Number(s): CONF-9404305--Vol.2; ON: DE96005736
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ITERATIVE METHODS
MATRICES
NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS