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A general algorithm for compressible and incompressible flows. Part III: the semi-implicit

机译:用于可压缩和不可压缩流的通用算法。第三部分:半隐式

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In this paper we consider some particular aspect related to the semi-implicit version of a fractional step finite element method for compressible flows that we have developed recently. The first is the imposition of boundary conditions. We show that no boundary conditions at all need to be imposed in the first step where an intermediate momentum is computed. This allows us to impose the real boundary conditions for the pressure, a point that turns out to be very important for compressible flows. The main difficulty of the semi-implicit form of the scheme arises in the solution of the continuity equation, since it involves both the density and the pressure. These two variables can be related through the equation of state, which in turn introduces the temperature as a variable in many cases. We discuss here the choice of variables (pressure or density) and some strategies to solve the continuity equation. The final point that we study is the behaviour of the scheme in the incompressible limit. It is shown that the method has a inherent pressure dissipation that allows us to reach this limit without having to satisfy the classical compatibility conditions for the interpolation of the velocity and the pressure.
机译:在本文中,我们考虑了与最近开发的可压缩流的分数步有限元方法的半隐式版本有关的某些特定方面。首先是施加边界条件。我们表明,在计算中间动量的第一步中,根本不需要施加任何边界条件。这使我们可以为压力施加实际的边界条件,这一点对于可压缩流来说非常重要。该方案的半隐式形式的主要困难出现在连续性方程的解中,因为它涉及密度和压力。这两个变量可以通过状态方程关联,而状态方程又将温度作为变量引入。我们在这里讨论变量(压力或密度)的选择以及一些解决连续性方程的策略。我们研究的最后一点是方案在不可压缩极限下的行为。结果表明,该方法具有固有的压力耗散,可以使我们达到此极限,而不必满足经典的相容性条件,即速度和压力的插值。

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