非线性BGK动能方程的投影积分法
Projective integration for nonlinear BGK kinetic equations
AI总结：
本文提出一种高阶全显式渐近保持投影积分方案，用于非线性BGK方程。通过简单显式方法抑制解的刚性成分，再用任意阶Runge-Kutta方法估计时间导数。基于线性化BGK算子谱，证明外时间步长限制与刚性源项无关。
摘要：
我们提出一种高阶、全显式、渐近保持的投影积分方案，用于非线性BGK方程。该方法首先用简单的显式方法（如直接前向欧拉法）进行几次小步长（内步）以抑制解的刚性成分。然后用任意阶的Runge-Kutta方法估计时间导数。基于线性化BGK算子的谱，我们推导出，当适当选择内步长时，外时间步长限制以及内时间步数的限制与BGK源项的刚性无关。我们通过一维和二维空间中的数值结果来说明该方法。
英文摘要：
We present a high-order, fully explicit, asymptotic-preserving projective integration scheme for the nonlinear BGK equation. The method first takes a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution. Then, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. Based on the spectrum of the linearized BGK operator, we deduce that, with an appropriate choice of inner step size, the time step restriction on the outer time step as well as the number of inner time steps is independent of the stiffness of the BGK source term. We illustrate the method with numerical results in one and two spatial dimensions.
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