Improving mass conservation in simulation of incompressible flows

• Published in: International journal for numerical methods in engineering Vol. 90; no. 12; pp. 1435 - 1451
• Main Authors: Ryzhakov, P., Oñate, E., Rossi, R., Idelsohn, S.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 22.06.2012; Wiley
• Subjects: Combinatorics; Combinatorics. Ordered structures; Computational methods in fluid dynamics; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; fractional step method; Fundamental areas of phenomenology (including applications); Graph theory; incompressible flows; Lagrangian fluids; mass conservation; Mathematical analysis; Mathematics; Ordinary differential equations; PFEM; Physics; pressure prediction; Sciences and techniques of general use; Performance evaluation; Lagrangian; Fluid-structure interactions; Lagrangian fluids; Fractional step method; Mass loss; Boundary conditions; Poisson equation; Momentum; Graph theory; incompressible flows; Fractional derivative; Conservation laws; Vibrations; Incompressible flow; mass conservation; Free surface flow; Modelling; Incompressible fluid; PFEM; Viscous fluids; pressure prediction; Mesh generation
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3370

SUMMARY We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian fluid formulation, where the mass loss effects are particularly apparent. However, the methodology is general and could be used for fixed grid approaches. The idea consists in reflecting the incompressibility condition already in the intermediate velocity. This is achieved by predicting the end‐of‐step pressure and using this prediction in the fractional momentum equation. The resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme. In turn, the predicted pressure can be used as the boundary condition necessary for the solution of the pressure Poisson equation in case a continuous Laplacian matrix is employed. Using this approximation of the end‐of‐step incompressible pressure as the essential boundary condition considerably improves the conservation of mass, specially for the free surface flows of fluids with low viscosity. The pressure prediction does not require the resolution of any additional equations system. The efficiency of the method is shown in two examples. The first one shows the performance of the method with respect to mass conservation. The second one tests the method in a challenging fluid–structure interaction benchmark, which can be naturally resolved by using the presented approach. Copyright © 2012 John Wiley & Sons, Ltd.