论文标题
用于旋转球体上不可压缩的Navier-Stokes方程的分析无差异搭配方法
An analytically divergence-free collocation method for the incompressible Navier-Stokes equations on the rotating sphere
论文作者
论文摘要
在这项工作中，我们使用radial基函数（RBF）开发了一种高阶搭配方法，用于旋转球体上不可压缩的Navier-Stokes方程（NSE）。该方法基于求解NSE对无差异函数空间的投影。为此，我们使用矩阵有价值的内核函数，允许对速度场进行分析无差异近似。使用导致无旋转近似值的内核函数，可以在其中一个发生的近似值中通过简单的内核交换来恢复压力，而无需解决其他泊松问题。我们建立了半差异解决方案的速度和压力函数的精确误差估计。最后，我们对数值成本进行了简短的估计，并将新方法应用于实验测试案例。
In this work, we develop a high-order collocation method using radial basis function (RBF) for the incompressible Navier-Stokes equation (NSE) on the rotating sphere. The method is based on solving the projection of the NSE on the space of divergence-free functions. For that, we use matrix valued kernel functions which allow an analytically divergence-free approximation of the velocity field. Using kernel functions which lead to rotation-free approximations, the pressure can be recovered by a simple kernel exchange in one of the occurring approximations, without solving an additional Poisson problem. We establish precise error estimates for the velocity and the pressure functions for the semi-discretised solution. In the end, we give a short estimate of the numerical cost and apply the new method to an experimental test case.
