高阶时间精度的
Higher-order in time "quasi-unconditionally stable" ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains
AI总结：
本文提出高阶时间精度（二到六阶）的交替方向隐式求解器，用于求解二维和三维曲面域中的可压缩纳维-斯托克斯方程，通过BDF方法和非线性项的外推技术实现高精度和稳定性。
摘要：
本文介绍了一种交替方向隐式（ADI）求解器，用于求解二维和三维曲面域中的可压缩纳维-斯托克斯方程，具有更高的时间精度（二到六阶）。高阶时间精度源于1）将后向差分公式时间步进算法（BDF）与2）用于某些非线性项的BDF-like外推技术相结合，以及3）一种新的道格拉斯-金分裂应用，这大大方便了边界条件的处理同时保持了高阶时间精度。根据我们对各种特殊情况的算法理论分析，大量数值实验表明，本文提出的基于BDF的ADI算法都是
英文摘要：
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas-Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are "quasi-unconditionally stable" in the following sense: each algorithm is stable for all couples $(h,Δt)$ of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form $(0,M_h)\times (0,M_t)$. In other words, for each fixed value of $Δt$ below a certain threshold, the Navier-Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier-Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier-Stokes solvers for which second order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions.
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