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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver
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Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver

机译：整体式有限元求解器中自适应时间积分器与自适应网格之间的相互作用

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Purpose This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing based on Zhu and Zienkiewicz error estimation approach. If mesh adaptation only occurs at user-supplied times and results in a completely new mesh, it is necessary to stop the time-integration at these same times. In these conditions, one challenge is to find an efficient and reliable way to restart the time-integration. The authors investigate what impact grid-to-grid interpolation errors have on the relaunch of the computation. Design/methodology/approach Two restart strategies of the time-integrator were used: one based on resetting the time-step size h and time-integrator order p to default values (used in the initial startup phase), and another designed to restart with the time-step size h and order p used by the solver prior to remeshing. The authors also investigate the benefits of quadratically interpolate the solution on the new mesh. Both restart strategies were used to solve laminar incompressible Navier-Stokes and the Unsteady Reynolds Averaged Naviers-Stokes (URANS) equations. Findings The adaptive features of our time-integrators are excellent tools to quantify errors arising from the data transfer between two grids. The second restart strategy proved to be advantageous only if a quadratic grid-to-grid interpolation is used. Results for turbulent flows also proved that some precautions must be taken to ensure grid convergence at any time of the simulation. Mesh adaptation, if poorly performed, can indeed lead to losing grid convergence in critical regions of the flow. Originality/value This study exhibits the benefits and difficulty of assessing both spatial error estimates and local error estimates to enhance the efficiency of unsteady computations.
机译：目的本文旨在着重描述基于后向差分公式（BDF）的hp自适应时间积分器与基于Zhu和Zienkiewicz误差估计方法的自适应网格划分之间的相互作用。如果网格自适应仅在用户提供的时间发生并导致全新的网格，则必须在这些相同的时间停止时间积分。在这种情况下，一个挑战是找到一种有效且可靠的方式来重新启动时间积分。作者研究了网格到网格内插误差对重新启动计算的影响。设计/方法/方法使用了时间积分器的两种重启策略：一种基于将时间步长h和时间积分器阶数p重置为默认值（在初始启动阶段中使用），另一种旨在通过以下方式重启：重新定型之前求解器使用的时间步长h和阶数p。作者还研究了在新网格上进行二次插值求解的好处。两种重启策略均用于求解层状不可压缩的Navier-Stokes和非稳态雷诺平均Naviers-Stokes（URANS）方程。结果我们的时间积分器的自适应功能是出色的工具，可用于量化由两个网格之间的数据传输引起的误差。仅当使用二次网格到网格插值时，第二重启策略才被证明是有利的。湍流的结果还证明，必须采取一些预防措施以确保在模拟的任何时候网格都收敛。网格自适应（如果执行效果不佳）的确会导致流的关键区域失去网格收敛性。独创性/价值本研究展示了评估空间误差估计和局部误差估计以提高非稳定计算效率的好处和困难。

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