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首页> 外文期刊>Applied Mathematical Modelling >An Eulerian-Lagrangian mixed discrete least squares meshfree method for incompressible multiphase flow problems
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An Eulerian-Lagrangian mixed discrete least squares meshfree method for incompressible multiphase flow problems

机译：不可压缩多相流问题的欧拉-拉格朗日混合离散最小二乘无网格方法

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摘要

Mixed discrete least squares meshfree (MDLSM) method has been developed as a truly meshfree method and successfully used to solve single-phase flow problems. In the MDLSM, a residual functional is minimized in terms of the nodal unknown parameters leading to a set of positive-definite system of algebraic equations. The functional is defined using a least square summation of the residual of the governing partial differential equations and its boundary conditions at all nodal points discretizing the computational domain. Unlike the discrete least squares meshfree (DLSM) which uses an irreducible form of the governing equations, the MDLSM uses a mixed form of the original governing equations allowing for direct calculation of the gradients leading to more accurate computational results. In this study, an Eulerian-Lagrangian MDLSM method is proposed to solve incompressible multiphase flow problems. In the Eulerian step, the MDLSM method is used to solve the governing phase averaged Navier-Stokes equations discretized at fixed nodal points to get the velocity and pressure fields. A Lagrangian based approach is then used to track different flow phases indexed by a set of marker points. The velocities of marker points are calculated by interpolating the velocity of fixed nodal points using a kernel approximation, which are then used to move the marker points as Lagrangian particles to track phases. To avoid unphysical clustering and dispersing of the marker points, as a common drawback of Lagrangian point tracking methods, a new approach is proposed to smooth the distribution of marker points. The hybrid Eulerian and Lagrangian characteristics of the approach used here provides clear advantages for the proposed method. Since the nodal points are static on the Eulerian step, the time-consuming moving least squares (MLS) approximation is implemented only once making the proposed method more efficient than corresponding fully Lagrangian methods. Furthermore, phases can be simply tracked using the Lagrangian phase tracking procedure. Efficiency of the proposed MDLSM multiphase method is evaluated using several benchmark problems and the results are presented and discussed. The results verify the efficiency and accuracy of the proposed method for solving multiphase flow problems. (C) 2019 Elsevier Inc. All rights reserved.
机译：混合离散最小二乘无网格（MDLSM）方法已发展为一种真正的无网格方法，并成功用于解决单相流问题。在MDLSM中，根据节点未知参数将残差泛函最小化，从而导致形成一组正定的代数方程组。使用控制偏微分方程的残差及其边界条件在所有节点上的最小二乘求和的最小二乘求和来定义计算域。与使用控制方程的不可约形式的离散最小二乘无网格（DLSM）不同，MDLSM使用原始控制方程的混合形式，可以直接计算梯度，从而获得更准确的计算结果。在这项研究中，提出了一种欧拉-拉格朗日MDLSM方法来解决不可压缩的多相流问题。在欧拉步骤中，使用MDLSM方法求解在固定节点处离散的控制相位平均Navier-Stokes方程，以获得速度和压力场。然后使用基于拉格朗日的方法来跟踪由一组标记点索引的不同流动阶段。标记点的速度是通过使用核近似值插值固定节点的速度来计算的，然后将其用作拉格朗日粒子来移动标记点以跟踪相位。为了避免标记点的非物理聚类和分散，作为拉格朗日点跟踪方法的共同缺点，提出了一种新的方法来平滑标记点的分布。此处使用的方法的混合欧拉和拉格朗日特性为所提出的方法提供了明显的优势。由于节点在欧拉阶上是静态的，因此仅执行一次耗时的移动最小二乘（MLS）近似即可，从而使该方法比相应的完全拉格朗日方法更有效。此外，可以使用拉格朗日相位跟踪程序简单地跟踪相位。使用几个基准问题评估了所提出的MDLSM多相方法的效率，并给出并讨论了结果。结果证明了所提方法解决多相流问题的效率和准确性。 （C）2019 Elsevier Inc.保留所有权利。

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