Numerical Solutions of Advection-Dominated Problems
When the advection term dominates in the advection-dispersion equation, most traditional numerical methods will encounter difficulties. In Chapter 4, we have stated that when the FDM is used for solving advection-dominated problems, two kinds of errors, numerical dispersion and overshoot, will occur. As a result, oscillations will appear around concentration fronts and steep concentration fronts cannot be accurately calculated. In Chapter 5, we pointed out that the Galerkin FEM cannot avoid the above two kinds of errors, either. Consequently, improvement of the accuracy and stability of numerical solutions has become an important subject in current research.
KeywordsPeclet Number Finite Difference Approximation Numerical Dispersion Finite Element Equation Move Coordinate System
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