SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization
Group of Numerical Methods in Engineering, Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain
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Water 2021, 13(3), 245; https://doi.org/10.3390/w13030245
Received: 11 December 2020
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Revised: 11 January 2021
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Accepted: 14 January 2021
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Published: 20 January 2021
(This article belongs to the Special Issue Computational Fluid Mechanics and Hydraulics)
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.
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Keywords:
high-order methods; smoothed particle hydrodynamics; meshless methods; multi-dimensional optimal order detection; moving least squares; weakly compressible
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MDPI and ACS Style
Eirís, A.; Ramírez, L.; Fernández-Fidalgo, J.; Couceiro, I.; Nogueira, X. SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization. Water 2021, 13, 245. https://doi.org/10.3390/w13030245
AMA Style
Eirís A, Ramírez L, Fernández-Fidalgo J, Couceiro I, Nogueira X. SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization. Water. 2021; 13(3):245. https://doi.org/10.3390/w13030245
Chicago/Turabian StyleEirís, Antonio, Luis Ramírez, Javier Fernández-Fidalgo, Iván Couceiro, and Xesús Nogueira. 2021. "SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization" Water 13, no. 3: 245. https://doi.org/10.3390/w13030245
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