论文标题
与边界不可压缩流体的傅立叶延续方法
Fourier continuation method for incompressible fluids with boundaries
论文作者
论文摘要
我们提出了一种基于傅立叶延续的平行伪谱法，用于在立方体非周期域中不可压缩的流体。该方法可产生域内快速频谱收敛的无分散和无耗散衍生物，并且在边界处具有非常高的收敛性。通过求解压力的泊松方程来实现不可压缩性。作为基于傅立叶的方法，该方法允许快速计算光谱变换。它与统一的网格兼容（尽管也可以实现精制或嵌套的网格），这又允许在足够高的雷诺数数字上明确集成时间。使用名为Specter的新的并行代码，我们说明了该方法有两个问题：通道流和Boussinesq近似下的平面雷利 - 贝纳德对流。在这两种情况下，该方法都会使用其他高阶数值方法与以前的研究兼容，对稳定性的时间步骤有轻度的要求。
We present a Fourier Continuation-based parallel pseudospectral method for incompressible fluids in cuboid non-periodic domains. The method produces dispersionless and dissipationless derivatives with fast spectral convergence inside the domain, and with very high order convergence at the boundaries. Incompressibility is imposed by solving a Poisson equation for the pressure. Being Fourier-based, the method allows for fast computation of spectral transforms. It is compatible with uniform grids (although refined or nested meshes can also be implemented), which in turn allows for explicit time integration at sufficiently high Reynolds numbers. Using a new parallel code named SPECTER we illustrate the method with two problems: channel flow, and plane Rayleigh-Bénard convection under the Boussinesq approximation. In both cases the method yields results compatible with previous studies using other high-order numerical methods, with mild requirements on the time step for stability.
