论文标题
部分可观测时空混沌系统的无模型预测
Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation
论文作者
论文摘要
在这项工作中，我们旨在构建数值方案，这些方案在成本和不变性的成本和保护方面都尽可能有效，对于vlasov--fokker- planck系统以及泊松或Ampère方程。使用分裂方法，如果空间中的线性项通过光谱或半拉格朗日方法处理，并且使用稳定的runge-kutta-kutta-chebyshev（rkc）集成符（一种强大的隐含方案替代方案）对碰撞操作员速度的非线性扩散进行处理。新方案被证明可以完全保留质量和动量。使用适当的电场近似获得总能量。在半混凝土情况下证明了H Theorem，而熵衰减的数值为完全离散的问题进行了说明。进行了数值实验，包括研究Landau阻尼现象和颠簸的不稳定性，以说明新方案的效率。
In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Ampère equation. Splitting methods are used where the linear terms in space are treated by spectral or semi-Lagrangian methods and the nonlinear diffusion in velocity in the collision operator is treated using a stabilized Runge--Kutta--Chebyshev (RKC) integrator, a powerful alternative of implicit schemes. The new schemes are shown to exactly preserve mass and momentum. The conservation of total energy is obtained using a suitable approximation of the electric field. An H-theorem is proved in the semi-discrete case, while the entropy decay is illustrated numerically for the fully discretized problem. Numerical experiments that include investigation of Landau damping phenomenon and bump-on-tail instability are performed to illustrate the efficiency of the new schemes.
