For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

A coupling method based on the overset grid approach has been successfully developed to
couple multi-copies of a massively-parallel unstructured compressible LES solver AVBP for …

We describe a numerical method for modeling temperature-dependent fluid flow coupled to
heat transfer in solids. This approach to conjugate heat transfer can be used to compute …

This paper describes an approach for the numerical solution of time-dependent partial
differential equations in complex three-dimensional domains. The domains are represented …

High-order accurate upwind approximations for the wave equation in second-order form on
overlapping grids are developed. Although upwind schemes are well established for first …

A major difficulty in finite element analysis is the preparation of an effective mesh leading to
a good response solution. In engineering analyses of complex components, oftentimes …

We describe an algorithm to easily and efficiently incorporate upwinding into finite-difference
schemes for solving wave equations in second-order form and apply this scheme to solve …

We consider fourth order accurate compact schemes, in both space and time, for the second
order wave equation with a variable speed of sound. We demonstrate that usually this is …

Energy-stable difference methods for hyperbolic initial–boundary value problems are
constructed using a Galerkin framework. The underlying basis functions are Lagrange …

An overlapping mesh methodology that is spectrally accurate in space and up to third-order
accurate in time is developed for solution of unsteady incompressible flow equations in three …