SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization

Abstract

A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.

A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

“…A Lagrangian approach and homogeneous boundary conditions are used for the proposed test cases, unless indicated in the text. The boundary conditions in this work were implemented using the mirroring ghost particles procedure, as in [47,48].…”

Computational Fluid Mechanics and Hydraulics

“…This Special Issue includes eleven original contributions, including nine research articles [1][2][3][4][5][6][7][8][9] and three review papers [10,11]. In terms of the modeling techniques, these papers develop and apply a variety of methods such as mesh-based Eulerian [1][2][3], meshfree Lagrangian [4,5,7,8], and data-driven [6] techniques.…”

“…This Special Issue includes eleven original contributions, including nine research articles [1][2][3][4][5][6][7][8][9] and three review papers [10,11]. In terms of the modeling techniques, these papers develop and apply a variety of methods such as mesh-based Eulerian [1][2][3], meshfree Lagrangian [4,5,7,8], and data-driven [6] techniques. These models are applied to study Water 2022, 14, 3985. https://doi.org/10.3390/w14243985 https://www.mdpi.com/journal/water different hydraulics problems, including curved channels [1,2,11], channel confluences [10], air-core vortices [5], and submerged granular slides [3].…”

“…The aim of the article by Eiris et al [7] is to extend the prior work of its authors in introducing an SPH stabilization technique for ideal gasses to the case of incompressible viscous flows. It is based on SPH and an Arbitrary Lagrangian-Eulerian (ALE) framework.…”

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

“…Contrary to the polynomial WENO above-mentioned, both Vergnaud et al [33] and Zhang et al [34] use 1D stencils along each interacting particle pair. Moreover, alternative methods to stabilize mesh-based schemes have been extended to SPH such as the a posteriori Multi-dimensional Optimal Order Detection (MOOD) technique [35].…”