Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored numerical schemes. The present work proposes a second order exponential integrator for the numerical solution of sonic-boom propagation modelled through a dispersive equation with Burgers' nonlinearity. The linear terms are efficiently solved in frequency space through FFT, while the nonlinear terms are efficiently solved by a WENO scheme. The numerical method is designed to be highly parallelisable and therefore takes full advantage of modern computer hardware. The new approach also improves the accuracy compared to the splitting method and it reduces oscillations. The enclosed numerical results illustrate that parallelisation on a CPU results in a speedup of 22 times faster than the straightforward sequential version. The GPU implementation further accelerates the runtime by a factor 3, which improves to 5 when single precision is used instead of double precision.
翻译:最近为模拟声波传播提出了一种分离方法。 分裂方法允许将复杂的部分差异方程式分成更简单的部分,由专门定制的数字方法解决。 目前的作品提议了第二个顺序指数集成器, 用于通过布尔格斯的非线性分散式方程式模拟音波传播的数字解决方案。 线性术语通过FFFT在频率空间中有效解决, 非线性术语由WENO方案有效解决。 数字方法的设计是高度平行的, 从而充分利用现代计算机硬件。 新的方法还提高了与分离方法的准确性, 并减少了振动。 附加的数字结果显示, CPU的平行化速度比直截式顺序版本快22倍。 GPU的实施进一步加快了运行时间, 以因使用单一精度而不是双精度而提高到5倍的因子 3 。