201	1997	Margot Gerritsen and Pelle Olsson	pelle@tdb.uu.se	Designing an Efficient Solution Strategy for Fluid Flows II: Stable High-Order Central Finite Difference Schemes on Composite Adaptive Grids with Sharp Shock Resolution

                               Abstract

A simple and efficient solution strategy is designed for fluid flows 
governed by the compressible Euler equations. It is constructed from a 
stable high-order central finite difference scheme on structured composite 
adaptive grids. This basic framework is suitable for solving smooth flows 
on complicated domains and is easily extendible with extra tools to handle 
specific flow problems. The stable high-order central difference scheme 
is mathematically formulated using a recently derived semi-discrete energy 
method for initial-boundary value problems. The high order of accuracy 
reduces the number of grid points required in smooth parts of the flow, 
which leads to efficiency in both computational time and memory. A local 
grid adaptation technique is used to increase the grid density where required.

Extra tools are developed for the sharp resolution of shocks. The grids are 
refined in the shock regions to retain accuracy. On the fine grids in these 
regions, an effective scalar artificial viscosity term is added to suppress 
spurious oscillations generated by the high-order central difference method. 
The location and orientation of shocks is determined by an easy-to-implement 
wavelet-based detection algorithm.

The overhead of the composite adaptive grid method and detection algorithm is 
negligible compared with the computational kernel. The local grid adaptation 
with the high-order scheme is shown to increase computational efficiency. 
The resolution of shocks is sharp.