Numerical Solution of Continuity Equations.
NAVAL RESEARCH LAB WASHINGTON D C
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This paper compares and contrasts the six general methods available for solving the time dependent continuity equation numerically. Since finite-difference techniques naturally arise as the most generally applicable solution methods, consideration is given to solving the major remaining difficulties encountered in the general application of Lagrangian and Eulerian finite differences. In the former, triangular mesh cells with free reconnections are suggested as a complicated but serviceable solution to the Lagrangian grid distortion problem. In the latter, nonlinear monotonic difference schemes are introduced as the natural way to avoid the Eulerian positivity problem. Flux-Corrected Transport techniques, the most developed and efficient of the positive monotone finite-difference approaches, are described with examples. Author
- Numerical Mathematics