In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers' system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov equation and local discontinuous Galerkin approximations for the viscous Burgers' equation. Both these methods use generalized numerical fluxes. The proposed scheme is both mass and momentum conservative. Based on generalized Gauss-Radau projections, optimal rates of convergence in the case of smooth compactly supported initial data are derived. Finally, computational results confirm our theoretical findings.

翻译：本文针对周期性Vlasov-粘性Burgers系统的逐步离散数值方案进行了开发和分析。 该方案基于Vlasov方程分段Galerkin逼近和粘性Burgers方程局部分段Galerkin逼近的耦合，两种方法都使用了广义数值通量。 建议的方案既保持质量又保持动量守恒。 基于广义Gauss-Radau投影，推导出在光滑紧支初值数据情况下的最优收敛速度。 最后，计算结果确认了我们的理论发现。