Abstract
A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.
Highlights
In this paper, given a two-dimensional bounded domain Ω in R2 with Lipschitz boundary Γ and a time interval 1⁄20, T, we are interested in solving the two-dimensional unsteady nonlinear coupled Burgers’ equations ! ∂u ∂t + u ∂u ∂x v ∂u ∂y − ν ∂2u ∂x2 ∂2u ∂y2
For all results reported the radius of the circle used in the radial basis functions (RBF) procedure is set to 2h, with h is the space stepsize
We have proposed a new cell-centered finite volume semiLagrangian method for the numerical solution of twodimensional coupled Burgers’ problems on unstructured triangular meshes
Summary
The main objective of the current study is to devise a numerical approach able to accurately approximate solutions of the coupled Burgers’ equations on unstructured triangular grids
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