Spectral multigrid methods with applications to transonic potential flow

Transonic Potential Flow Calculations by Two Artificial Density Methods

A steady transonic flow over an airfoil is computed by solving the full potential equation discretized over a contour-fitting grid in full conservation form. Near shock waves, density is corrected to account for the rise in entropy in the region. A multigrid alternating direction method is used to drive the iteration. In supersonic flow regions, artificial dissipation is introduced by retarding...

An algebraic multigrid solver for transonic flow problems

This article presents the latest developments of an algebraic multigrid (AMG) based on full potential equation (FPE) solver for transonic flow problems with emphasis on advanced applications. The mathematical difficulties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic flow) to hyperbolic (supersonic flow). The flow solver is capa...

Relaxation Schemes for Chebyshev Spectral Multigrid Methods

SUMMARY Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The rst scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an eecient and relatively simple approach for solving two-dimensional spectral equations. Numerica...

Spectral Multigrid Methods for Elliptic Equations Ii

Multigrid methods for compressible laminar flow