Publication Results

Code: MOX 63
Title: A flux form, semi - Lagrangian method for the scalar advection equation usign Discontinuous Galerkin reconstruction
Date: Wednesday 1st June 2005
Author(s) : Restelli, Marco; Bonaventura, Luca; Sacco, Riccardo
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Abstract: A new semi Lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form. The approach combines the accuracy and flexibility of the Discontinuous Galerkin method with the computational efficiency and robustness of Semi-Lagrangian techniques. Unconditional stability of the proposed discretization is proven in the Von Neumann sense for the one dimensional case. A monotonization technique is then introduced, based on the Flux Corrected Transoport approach. This yields a multidimensional monotonic scheme for the piecewise constant component of the computed solution, while reducing the numerical diffusion of monotonization approaches more common in the Discontinuous Galerkin framework. The accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests. The comparison with results obtained by standard semi - Legrangian and Discontinuous Galerkin methods highlights several computational advantages of the new technique.

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M.Restelli, L. Bonaventura and R. Sacco,A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows, Journal of Computational Physics,Vol. 216, pp. 195-215, 2006