Abstract
Most slope limiter functions in high-resolution finite volume methods to solve hyperbolic conservation laws are designed assuming one-dimensional uniform grids, and they are also used to compute slope limiters in computations on nonuniform rectilinear grids. However, this strategy may lead to either loss of the total variation diminishing (TVD) stability for one-dimensional linear problems or loss of formal second-order accuracy if the grid is highly nonuniform. This is especially true when the limiter function is not piecewise linear. Numerical evidence is provided to support this argument for two popular finite volume strategies: monotonic upstream-centered scheme for conservation laws in space and method of lines in time (MUSCL-MOL) and capacity-form differencing. In order to deal with this issue, this paper presents a general approach to study and enhance the slope limiter functions for highly nonuniform grids in the MUSCL-MOL framework. This approach extends the classical reconstruct-evolve-project p...
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