用于Vlasov模拟的一类基于混合HWENO的转秩直线法

A hybrid HWENO-based method of lines transpose approach for Vlasov simulations

在隐式转秩直线法(MOLT)框架下,针对一维线性输运方程设计了一类新型的混合Hermite加权本质无震荡(HWENO)格式,并进一步用于求解Vlasov-Poisson(VP)方程组.相较于之前的基于加权本质无震荡(WENO)的MOLT方法[J.Comput.Phys.,2016,327:337-367],该新方法主要有两个优点:第一,在满足相同精度的情况下,HWENO格式比WENO格式使用更窄的模版;第二,该方法可以自动调节选取线性格式或HWENO格式.因此,混合HWENO方法既保持了WENO方法的简便性和鲁棒性,同时,又能在光滑区域减小计算误差,降低计算时间,提高计算效率.我们将设计的算法用于模拟一系列基准算例,以展示其鲁棒性和高效性.

A new type hybrid Hermite weighted essentially non-oscillatory(HWENO)schemes in the implicit method of lines transpose(MOLT)framework is designed for solving one-dimensional linear transport equations and further applied to the Vlasov-Poisson(VP)simulations via dimensional splitting.Compared with the WENO-based MOLT method given in J.Comput.Phys.[2016,327:337-367],the new proposed hybrid HWENO-based MOLT scheme has two advantages.The first is the HWENO schemes using the stencils narrower than those of the WENO schemes with the same order of accuracy.The second is that the schemes can adapt between the linear scheme and the HWENO scheme automatically.In summary,the hybrid HWENO scheme keeps the simplicity and robustness of the simple WENO scheme,while it has higher efficiency with less numerical errors in smooth regions and less computational costs as well.Benchmark examples are given to demonstrate the robustness and good performance of the proposed scheme.