Numerical analysis of a fractional step theta-method for fluid flow problems
作者： John C. Chrispell
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摘要: The accurate numerical approximation of viscoelastic fluid flow poses two difficulties: the large number unknowns in approximating algebraic system (corresponding to velocity, pressure, and stress), different mathematical types modeling equations. Specifically, equations have a hyperbolic constitutive equation coupled parabolic conservation momentum equation. An appealing approach is use fractional step θ-method. θ-method an operator splitting technique that may be used decouple as well separate updates distinct variables when mixed systems partial differential In this work described analyzed for computation both time dependent convection-diffusion using Johnson-Segalman model. For presented allows decoupling within steps diffusion from convection operator. update stabilized Streamline Upwinded Petrov-Galerkin (SUPG)-method. analysis given serves template more complicated implementation velocity pressure approximations decoupled stress, reducing resolved at each method. Additionally results nonlinear only solution linear Similar scheme implemented convection-diffusion, SUPG-method. priori error estimates are established their approximations. Numerical
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