Solving the unsteady linear advection diffusion equations by using the totally volume in- tegral of the local discontinuous Galerkin method. 1

Abstract

Abstract

In this paper, we present the totally volume integral of the local discontinuous Galerkin TV LDG method to solve the time-dependent linear convection-diffusion equation, the considered equation is discretized in space by the local discontinuous Galerkin method after the boundaries integral is transformed into the volume integral by employing the divergence theorem. The time discretization is accomplished by the third-order strong stability preserving Runge Kutta explicit SSP-RK (3, 3) method. Numerical solutions are compared with analytical solutions and other methods. The obtained results show that the totally volume integral of the local discontinuous Galerkin method is one of the most efficient methods for solving the time-dependent linear advection-diffusion equations 

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