Skeleton-stabilized immersogeometric analysis for incompressible viscous 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...

Procedures for solving spectral/hp stabilized incompressible flow problems

In this paper we implement the element-by-element preconditioner and inexact Newton-Krylov methods (developed in the past) for solving stabilized computational fluid dynamics (CFD) problems with spectral methods. Two different approaches are implemented for speeding up the process of solving both steady and unsteady incompressible Navier-Stokes equations. The first approach concerns the applica...

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 ...

Parallel Adaptive Simulation of Coupled Incompressible Viscous Flow and Advective-Diffusive Transport Using Stabilized FEM Formulation

In this work we study coupled incompressible viscous flow and advective-diffusive transport of a scalar. Both the Navier-Stokes and transport equations are solved using an Eulerian approach. The SUPG/PSPG stabilized finite element formulation is applied for the governing equations. The implementation is held using the libMEsh finite element library which provides support for parallel adaptive m...

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