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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations
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An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations

机译：Navier-Stokes方程二阶时间步长方法的最优精确离散正则化

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摘要

We propose a new, optimally accurate numerical regularization/stabilization for (a family of) second order timestepping methods for the Navier-Stokes equations (NSE). The method combines a linear treatment of the advection term, together with stabilization terms that are proportional to discrete curvature of the solutions in both velocity and pressure. We rigorously prove that the entire new family of methods are unconditionally stable and O(Delta t(2)) accurate. The idea of 'curvature stabilization' is new to CFD and is intended as an improvement over the commonly used 'speed stabilization', which is only first order accurate in time and can have an adverse effect on important flow quantities such as drag coefficients. Numerical examples verify the predicted convergence rate and show the stabilization term clearly improves the stability and accuracy of the tested flows. (C) 2016 Elsevier B.V. All rights reserved.
机译：我们为Navier-Stokes方程（NSE）的（一族）二阶时间步长方法提出了一种新的，最精确的数值正则化/稳定化方法。该方法将对流项的线性处理与与速度和压力中的溶液的离散曲率成比例的稳定项结合在一起。我们严格证明，整个新方法族都是无条件稳定的并且O（Delta t（2））准确。 “曲率稳定”的概念是CFD的新概念，旨在对常用的“速度稳定”进行改进，后者在时间上仅一阶准确，并且可能对重要的流量（例如阻力系数）产生不利影响。数值算例验证了预测的收敛速度，并表明稳定项明显提高了测试流的稳定性和准确性。 （C）2016 Elsevier B.V.保留所有权利。

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