The numerical simulation of two-dimensional fluid flow with strong shocks

Simple adaptive grids for 1-d initial value problems

During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut 'best' algorithm, several conclusions can be made. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results.

Numerical advection algorithms and their role in atmospheric transport and chemistry models

/pdf/numerical-methods-for-tracking-interfaces-489ml8y17q.pdf

S.K Doss

Papers

The moving finite element method: Applications to general partial differential equations with multiple large gradients☆