An efficient characteristic Galerkin scheme for the advection equation in 3-D

Conventional Galerkin-based finite element algorithms perform poorly when modeling advective transport. Here we develop and test a characteristic Galerkin scheme to solve the unsteady three-dimensional advective transport equation. The algorithm uses tracking of the Gaussian quadrature points to project the information from the Eulerian background grid to the Lagrangian grid. Numerical experiments were carried out to investigate the performance of this scheme. Despite speculations to the contrary in the literature, this scheme does not suffer from instability problems. Further, it is conservative, and shows good phase characteristics with slight numerical diffusion. We conclude that the characteristic Galerkin method is a viable and efficient scheme for solving advection problems in three dimensions.

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