Abstract
We explore how the weighted average flux approach can be used to generate first- and second-order accurate finite volume schemes for the linear advection equatons in one, two, and three space dimensions. The derived schemes have multidimensional upwinding aspects and good stability properties. From the two-dimensional methods, we construct a scheme for nonlinear systems of hyperbolic conservation laws that is second-order accurate in smooth flow. Spurious oscillations are controlled by making use of one-dimensional TVD limiter functions. Numerical results are presented for the shallow water equations in two space dimensions. The equivalent schemes are derived for nonlinear systems in three space dimensions.
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