二次非线性方程的高阶低存储显式Runge-Kutta格式
High-order low-storage explicit Runge-Kutta schemes for equations with quadratic nonlinearities
摘要：
在本文中，我们表明，三阶和四阶低存储龙格库塔算法可以专门为二次非线性算子，在大约一倍的时间所需的时间为代价，评估的时间导数。所得到的算法特别适合于计算流体动力学。例子给出的Hénon-Heiles哈密顿系统，并在一个和两个空间维度，为Burgers方程使用伪谱码和谱元码，分别。该方案也被证明是实用的，在三个空间求解不可压缩欧拉方程使用一个完全并行化的伪谱代码。
英文摘要：
We show in this paper that third- and fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives. The resulting algorithms are especially well suited for computational fluid dynamics. Examples are given for the Hénon-Heiles Hamiltonian system and, in one and two space dimensions, for the Burgers equation using both a pseudo-spectral code and a spectral element code, respectively. The scheme is also shown to be practical in three space solving the incompressible Euler equation using a fully parallelized pseudo-spectral code.
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