Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Journal of Computational Physics
A first-order system approach for diffusion equation. I: Second-order residual-distribution schemes
Journal of Computational Physics
On uniformly high-order accurate residual distribution schemes for advection-diffusion
Journal of Computational and Applied Mathematics
A first-order system approach for diffusion equation. II: Unification of advection and diffusion
Journal of Computational Physics
Journal of Scientific Computing
First-, second-, and third-order finite-volume schemes for diffusion
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we propose to write a source term in the divergence form. A conservation law with a source term can then be written as a single divergence form. We demonstrate that it enables to discretize both the conservation law and the source term in the same framework, and thus greatly simplifies the construction of numerical schemes. To illustrate the advantage of the divergence formulation, we apply the new formulation to construct a uniformly third-order accurate edge-based finite-volume scheme for conservation laws with a source term. Third-order accuracy is demonstrated for regular and irregular triangular grids for the linear advection and Burgers' equations with a source term.