具有耗散进口/出口条件的增强变量的内部不可压缩流的数值模拟。第1部分：数学公式和求解方法
Numerical simulation of internal incompressible flows with enhanced variants of dissipative inlet/outlet conditions. Part 1: Mathematical formulations and solution methods
摘要：
本文提出了粘性不可压缩流体在多进出口截面内区域非定常流动的数值方法。在流域的入口/出口处使用由惯性项增强的耗散边界条件的新变体。体积流率或入口/出口平均压力被施加为施加在流体运动上的附加约束。给出了具有这种条件和约束的Stokes问题的变分形式，并给出了求解方法。这些方法是基于叠加适当定义的辅助斯托克斯问题。扩展所提出的方法的Navier-Stokes流，基于运营商集成因子分裂（OIFS）技术，也进行了说明。接下来，一个非线性扩展的惯性耗散条件制定和纳入的解决方案框架的Navier-Stokes流。最后，一种替代的方法来流问题，这样的条件下，基于最优控制理论和伴随评估的目标功能梯度，提出。关于数字执行问题的几点意见制定。
英文摘要：
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at the inlets/outlets of the flow domain. Volumetric flow rates or inlet/outlet average pressure are imposed as additional constrains imposed on a fluid motion. The variational formulations of the Stokes problem with such conditions and constrains are presented and the solution methods are proposed. These methods are based on superposition of appropriately defined auxiliary Stokes problems. Extension of the proposed methodology to the Navier-Stokes flows, based on the Operator-Integration-Factor-Splitting (OIFS) technique, is also described. Next, a nonlinear extension of the inertial-dissipative conditions is formulated and incorporated in the solution framework for the Navier-Stokes flows. Finally, an alternative approach to flow problems with such conditions, based on optimal control theory and adjoint evaluation of the goal functional gradient, is presented. A few remarks concerning numerical implementation issues are formulated.
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