论文标题
具有生物三相层次基础函数的质量质量稀疏网格组合技术用于动力学模拟
A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations
论文作者
论文摘要
血浆湍流的确切数值模拟是融合研究中的资产和挑战之一。对于基于网格的求解器，由于维度的诅咒，通常无法实现的分辨率是无法实现的。稀疏的网格组合技术提供了减轻动力学模拟维度的诅咒的手段。但是，结合步骤与最先进的帽子功能的层次表示遭受了较差的保护特性和数值不稳定性。 目前的工作介绍了层次多尺度函数的两个新变体，用于与组合技术一起使用：生物表现和完整的加权基础。新的基础功能可节省总质量，并显示出有限体积固定溶液的恒定对流溶液的精度显着提高。基于应用于半拉格朗日vlasov的组合技术的进一步的数值实验表明，新碱基对模拟的稳定效果。
The exact numerical simulation of plasma turbulence is one of the assets and challenges in fusion research. For grid-based solvers, sufficiently fine resolutions are often unattainable due to the curse of dimensionality. The sparse grid combination technique provides the means to alleviate the curse of dimensionality for kinetic simulations. However, the hierarchical representation for the combination step with the state-of-the-art hat functions suffers from poor conservation properties and numerical instability. The present work introduces two new variants of hierarchical multiscale basis functions for use with the combination technique: the biorthogonal and full weighting bases. The new basis functions conserve the total mass and are shown to significantly increase accuracy for a finite-volume solution of constant advection. Further numerical experiments based on the combination technique applied to a semi-Lagrangian Vlasov--Poisson solver show a stabilizing effect of the new bases on the simulations.
