Accurate and efficient computation of steady water flow with surface waves and turbulence

A surface capturing method is developed for steady water-air flow with gravity. Second-order accuracy is obtained with flux limiting and turbulence is modeled with Menter's model. The model is solved efficiently with a combination of multigrid and defect correction. Results for two test cases confirm the efficiency and accuracy of the method.

Robust aggregation-based coarsening for additive Schwarz in the case of highly variable coefficients

We study two-level overlapping domain decomposition preconditioners with coarse spaces obtained by smoothed aggregation in iterative solvers for finite element discretisations of second-order elliptic problems. We are particularly interested in the situation where the diffusion coefficient (or the permeability) is highly variable throughout the...

Fictitious Boundary and Moving Mesh Methods for the Numerical Simulation of Particulate Flow

This paper discusses numerical simulation techniques using a moving mesh approach together with the multigrid fictitious boundary method (FBM) for liquid-solid flow configurations. The flow is computed by an ALE formulation with a multigrid finite element solver (FEATFLOW), and the solid particles are allowed to move freely through the...

A High Scalability Parallel Algebraic Multigrid Solver

This paper deals with the implementation and performance analysis of a parallel Algebraic Multigrid Solver (pAMG) for a finite volume unstructured CFD code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm. The Message passing interface Library (MPI) is used for...

Multigrid for High-Dimensional Elliptic Equations

This paper discusses multigrid for high dimensional partial differential equations (PDEs). We present partial grid-coarsening strategies for excellent multigrid convergence in the context of elliptic PDEs. We show that the multigrid convergence rate can satisfactorily be brought down with the grid strategies proposed herein, coupled with...

Multigrid Methods for Partial Differential Equations Arising From Fluid Flow Problems

In the paper, we present multigrid methods for solving scalar conservation laws and convection diffusion equations that frequently arise from fluid flow problems. For scalar conservation laws, we present monotonicity preserving and total variation diminishing multigrid methods. We generalize the upwind-biased residual restriction and...

On a decoupled algorithm for poroelasticity and its resolution by multigrid

In this work, we present a robust and efficient multigrid solver for a reformulated version of the system of poroelasticity equations. The reformulation enables us to treat the system in a decoupled fashion. It is sufficient to choose a highly efficient multigrid method for a scalar Poisson type equation for the overall solution of this...

A comparison between a direct and a multigrid sparse linear solvers for highly heterogeneous flux computations

Subsurface hydraulic properties are mainly governed by the heterogeneity of the porous medium considered. Our work aims at characterizing the asymptotic dispersion coefficients for highly heterogeneous permeability fields triggered by advection and constant local dispersion-diffusion. We have developed a fully parallel software for simulating...

A preconditioner for the Helmholtz equation with perfectly matched layer

This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace...

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...

Fast multigrid solution of optimal control problems with terminal observation

Recent developments on multilevel schemes for open-loop optimal control problems with terminal observation governed by time-dependent reaction-diffusion systems are presented. The solution of optimality systems consisting of reaction-diffusion equations with opposite time orientation is discussed. Of particular importance in applications and for...

Improving multigrid for 3-D electro-magnetic diffusion on stretched grids

We evaluated multigrid techniques for 3D diffusive electromagnetism. The Maxwell equations and Ohm's law were discretised on stretched grids, with stretching in all coordinate directions. We compared standard multigrid to alternative multigrid approaches with linewise smoothing and semi-coarsening, both as a stand-alone solver and as a...

Analysis of a hybrid p-Multigrid method for the discontinuous Galerkin discretisation of the Euler equations

A hybrid implicit and explicit p-Multigrid iteration strategy for the discretisation of the steady Euler equations with the discontinuous Galerkin finite element method is presented. The implicit strategy consists of an inexact damped Newton iteration, using an ILU(0)-preconditioned GMRES method for the solution of the linear system. Since the...

Coarse grid approximation governed by local

Solving discrete boundary value problems with the help of an appropriate multigrid method [1, 3, 4, 5] necessitates the construction of a sequence of coarse grids with corresponding coarse grid approximations for the given fine grid discretization. Popular choices in this context are the Galerkin coarse grid approximation (GCA) and the use of...

Towards an algebraic multigrid method for tomographic image reconstruction -- improving convergence of ART

In this paper we introduce a multigrid method for sparse, possibly rank-deficient and inconsistent least squares problems arising in the context of tomographic image reconstruction. The key idea is to construct a suitable AMG method using the Kaczmarz algorithm as smoother. We first present some theoretical results about the correction step and...