Adaptive Defect-Correction Methods for Viscous Incompressible Flow Problems

Adaptive Defect-Correction Methods for Viscous Incompressible Flow Problems

We consider a defect correction method (DCM) which has been used extensively in applications where solutions have sharp transition regions, such as high Reynolds number fluid flow problems. A reliable a posteriori error estimator is derived for a defect correction method. The estimator is further studied for two examples: (a) the case of a linear-diffusion, nonlinear convection-reaction equatio...

Numerical Methods for Incompressible Viscous Flow

We present an overview of the most common numerical solution strategies for the incompressible Navier–Stokes equations, including fully implicit formulations, artificial compressibility methods, penalty formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular operator splitting methods as special cases of a fully ...

An Adaptive Mesh Projection Method for Viscous Incompressible Flow

Many uid ow problems of practical interest|particularly at high Reynolds num-ber|are characterized by small regions of complex and rapidly-varying uid motion surrounded by larger regions of relatively smooth ow. EEcient solution of such problems requires an adaptive mesh reenement capability to concentrate computational eeort where it is most needed. We present in this paper a fractional-step v...

Algebraic Flux Correction III Incompressible Flow Problems

This chapter illustrates the use of algebraic flux correction in the context of finite element methods for the incompressible Navier-Stokes equations and related models. In the convection-dominated flow regime, nonlinear stability is enforced using algebraic flux correction. The numerical treatment of the incompressibility constraint is based on the ‘Multilevel Pressure Schur Complement’ (MPSC)...

On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems