Monolithic multigrid for implicit Runge–Kutta discretizations of incompressible fluid flow

Monolithic Newton-multigrid solution techniques for incompressible nonlinear flow models ⋆

We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretised by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviour but also regardin...

A Monolithic Ale Newton-krylov Solver with Multigrid-richardson-schwarz Preconditioning for Incompressible Fluid Structure Interaction

In this paper we study a monolithic Newton-Krylov solver with exact Jacobian for the solution of incompressible FSI problems. A main focus of this work is on the use of geometric multigrid preconditioners with modified Richardson smoothers preconditioned by an additive Schwarz algorithm. The definition of the subdomains in the Schwarz smoother is driven by the natural splitting between fluid an...

An Alternating Direction Implicit Method for Modeling of Fluid Flow

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

A New Implicit Algorithm with Multigrid for Unsteady Incompressible Flow Calculations

Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems

We present a block preconditioner for LDG discretizations of Stokes equations. The dependence of its performance on the discretization parameters is investigated. An extension to Oseen equations is shown, yielding efficient and robust solvers in a wide regime of Reynolds numbers.