论文标题
估计机器零残差
On Estimating Machine-Zero Residual
论文作者
论文摘要
在本文中，我们提出了两种技术来估计给定问题的机器零残差的大小，这是当我们求解离散方程系统时，可以实现的最小残留物。我们通过用随机扰动的近似解决方案计算出的残差标准来估计机器零残差的大小，该差距被认为是与精确交配的溶液的幅度。一种方法使用自由流动值作为近似解决方案，另一种方法在迭代求解过程中通过制造解决方案的方法使用当前解决方案。数值结果表明，这些估计值非常准确地预测了机零残差的水平，对于跨气管上的跨气流中的Euler和Navier-Stokes方程的所有方程式都非常准确，并在圆柱上和平板上粘着粘性流动。
In this paper, we propose two techniques to estimate the magnitude of a machine-zero residual for a given problem, which is the smallest possible residual that can be achieved when we solve a system of discretized equations. We estimate the magnitude of the machine-zero residual by a norm of residuals computed with a randomly-perturbed approximate solution that is considered as close in magnitude to an exactly-converged solution. One method uses free-stream values as the approximate solution, and the other uses a current solution during an iterative solve as the approximate solution via the method of manufactured solutions. Numerical results show that these estimates predict the levels of machine-zero residuals very accurately for all equations of the Euler and Navier-Stokes equations in a transonic flow over an airfoil and viscous flows over a cylinder and a flat plate.
