Advection simulation by minimaxcharacteristics method

The advective transport of a scalar is simulated by using the minimaxcharacteristics method, which is an explicit and efficient finite difference scheme derived from the local minimax approximation of the exact solution of the pure advection equation. Fourier mode analysis shows that the method is unconditionally stable, and produces relatively small celerity error and little amplitude dissipation. The scheme compares favorably with the other commonly used backward characteristics schemes', it is better than the scheme using quadratic interpolation (higher accuracy, approximately equal computational effort), and is better than the schemes using cubic interpolation (approximately equal accuracy, less computational effort); it is less accurate than the scheme using Hermitian cubic interpolation, but requires only one-half the computational effort. By interpreting the scheme as a backward characteristics scheme with quadratic approximation of the exact solution over four nodes, the extension of the method in a split-operator approach for advection-dispersion and hydrodynamics modeling in two or three dimensions is straightforward.