William D. Henshaw

Composite overlapping meshes for the solution of partial differential equations

Abstract We discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them. A composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet. Continuity conditions (interpolation) are imposed at the overlapping boundaries. The principal advantage of composite grids is in the generation of grids for regions with complicated geometries. The grid construction program CMPGRD is used to create composite grids with any number of component grids. We describe some techniques for the solution of elliptic and time-dependent PDEs on composite meshes. Applications to the solution of the compressible Navier-Stokes equations are presented.

Summing logarithmic expansions for singularly perturbed eigenvalue problems

Strong localized perturbations of linear and nonlinear eigenvalue problems in a bounded two-dimensional domain D are considered. The effects on an eigenvalue

Smallest scale estimates for the Navier-Stokes equations for incompressible fluids

lambda _0

A fourth-order-accurate difference approximation for the incompressible Navier-Stokes equations☆

of the Lapla-cian, and on the fold point

On the smallest scale for the incompressible Navier-Stokes equations

lambda _{c0}

Overture: object-oriented tools for overset grid applications

of a nonlinear eigenvalue problem, of removing a small subdomain

Numerical Experiments on the Interaction Between the Large- and Small-Scale Motions of the Navier-Stokes Equations

D_epsilon

A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids

, of “radius”

Conservation on composite overlapping grids

epsilon

On composite overlapping grids

, from D and imposing a condition on the boundary of the resulting hole, are determined. Using the method of matched asymptotic expansions, it is shown that the expansions of the eigenvalues and fold points for these perturbed problems start with infinite series in powers of