论文标题
四阶保守性非分类半拉格朗日式HERMITE WENO方案，用于动力学和流体模拟
Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations
论文作者
论文摘要
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov-Poisson system, the guiding center Vlasov model, and the incompressible Euler equations in the vorticity-stream function formulation.提出的SL Hweno方案将特征性盖尔金方法的弱公式与两种新构建的Hweno重建方法结合在一起。在非分类设置下，在空间和时间上都可以完成四阶精度。由于特征性盖尔金方法的表述弱和Hweno重建的设计，因此自然而然地保持了质量保护。我们应用一个肯定的限制器，以在需要时保持数值解决方案的阳性。尽管提出的SL框架使我们能够采取大量时间步骤来提高计算效率，但它也带来了空间重建技术的挑战。我们构建了两种新型的Hweno重建，以满足对拟议的SL框架的需求。进行了丰富的基准测试，以验证所提出的SL Hweno方案的有效性。
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov-Poisson system, the guiding center Vlasov model, and the incompressible Euler equations in the vorticity-stream function formulation. The proposed SL HWENO schemes combine a weak formulation of the characteristic Galerkin method with two newly constructed HWENO reconstruction methods. Fourth-order accuracy is accomplished in both space and time under a non-splitting setting. Mass conservation naturally holds due to the weak formulation of the characteristic Galerkin method and the design of the HWENO reconstructions. We apply a positive-preserving limiter to maintain the positivity of numerical solutions when needed. Although the proposed SL framework allows us to take large time steps for improving computational efficiency, it also brings challenges to the spatial reconstruction technique; we construct two kind of novel HWENO reconstructions to fit the need for the proposed SL framework. Abundant benchmark tests are performed to verify the effectiveness of the proposed SL HWENO schemes.
