A characteristics-mixed finite element method for advection-dominated transport problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions
SIAM Journal on Scientific Computing
Random walk particle tracking simulations of non-Fickian transport in heterogeneous media
Journal of Computational Physics
A fourth-order numerical scheme for solving the modified Burgers equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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Eulerian-Lagrangian localized adjoint method (ELLAM) is used to solve the advection diffusion equation (ADE) which is a very common mathematical model in physics. In this work, ELLAM is extended to triangular meshes. Standard integration schemes, which perform well for rectangular grids, are improved to reduce oscillations with unstructured triangulations. Numerical experiments for grid Peclet numbers ranking from 1 to 100 show the efficiency of the developed scheme. A new algorithm is also developed in order to avoid excessive numerical diffusion when using many time steps with the ELLAM. The basic idea of this approach is to keep the same characteristics for all time steps and to interpolate only the concentration variations due to the dispersion process at the end of each time step. Although ELLAM requires a lot of integration points for unstructured meshes, it remains a competitive method when using a single or many time steps compared to explicit discontinuous Galerkin finite element method.