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首页> 外文期刊>International Journal for Numerical Methods in Fluids >An algorithm for the simulation of thermally coupled low speed flow problems
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An algorithm for the simulation of thermally coupled low speed flow problems

机译：热耦合低速流动问题的仿真算法

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摘要

In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier-Stokes equations, written in nonconservation form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum-continuity system. If an explicit single-step time integration scheme for the energy equation is used, the decoupling results to be natural. Integration of the momentum-continuity system is carried out using a semi-explicit method, combining Runge-Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution. The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum-continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge-Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme. The method is tested using two benchmark examples.
机译：在本文中，我们提出了一种用于求解亚音速状态下热耦合流的计算算法。该公式基于以非保守形式编写的可压缩Navier-Stokes方程。通过分别求解能量方程，然后将计算出的温度用作动量连续性系统中的已知值，可以获得有效的模块化实现。如果对能量方程使用显式的单步时间积分方案，则解耦结果很自然。动量连续性系统的积分是使用半显式方法进行的，分别将Runge-Kutta方法和Backward Euler方案结合用于动量和连续性方程。即使在低马赫数（Ma 1）的情况下，对压力的隐式处理也会导致有利的时间步长估计。 Backward Euler方案引入的数值耗散确保了数值解中不存在杂散高频。该方法的重点是假设温度在一个时间步长内线性变化。结合动量连续性系统的部分拆分，它允许每个时间步仅解决一次连续性。忽略在Runge-Kutta方案的每个中间步骤中求解压力的必要性，可以最小化与隐式步骤相关的计算成本，并导致效率接近纯显式方案。使用两个基准示例测试了该方法。

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