SOLUTION OF THE IMPLICITLY DISCRETIZED FLUID-FLOW EQUATIONS BY OPERATOR-SPLITTING
SOLUTION OF THE IMPLICITLY DISCRETIZED FLUID-FLOW EQUATIONS BY OPERATOR-SPLITTING
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DOI：
10.1016/0021-9991(86)90099-9
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发表时间：
1986-01-01
影响因子：
4.1
通讯作者：
ISSA, RI
中科院分区：
文献类型：
--
作者：
ISSA, RI
本文提出了一种非迭代方法来处理隐式离散的含时流体流动方程的耦合问题。该方法是基于使用压力和速度作为因变量，因此适用于可压缩和不可压缩版本的输运方程。该技术的主要特点是分裂成一系列的步骤，从而对压力的操作是解耦的速度在每一步的解决方案的过程中，分裂的方程组是服从标准技术的解决方案。在每一个时间步，该程序产生的解决方案，近似的差分方程的精确解。这种分裂过程的准确性进行评估的线性形式的离散方程，分析表明，它产生的解决方案不同的精确解的差分方程的时间步长的权力成比例的条款。凭借这一点，它是可能的，以免除迭代，从而导致在一个有效的隐式计划，同时保持相对于当代块同步方法的实现简单性。这是验证在一个配套文件，其中提出了使用该方法进行计算的结果。
A non-iterative method for handling the coupling of the implicitly discretised time-dependent fluid flow equations is described. The method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations. The main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step, with the split sets of equations being amenable to solution by standard techniques. At each time-step, the procedure yields solutions which approximate the exact solution of the difference equations. The accuracy of this splitting procedure is assessed for a linearised form of the discretised equations, and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time-step size. By virtue of this, it is possible to dispense with iteration, thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods. This is verified in a companion paper which presents results of computations carried out using the method.