SPH with the multiple boundary tangent method

• Published in: International journal for numerical methods in engineering 2009-03, Vol.77 (10), p.1416-1438
• Main Authors: Yildiz, M., Rook, R. A., Suleman, A.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; flow over a cylinder; Fluid dynamics; Fundamental areas of phenomenology (including applications); incompressible SPH; Laminar flows; Laminar flows in cavities; lid-driven cavity; Physics; projective methods; smoothed particle hydrodynamics; Turbulent flows, convection, and heat transfer; Wakes
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2458

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid‐driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved solid boundaries, but the approach presented herein should be extendable to time‐evolving, free‐surface boundaries. Copyright © 2008 John Wiley & Sons, Ltd.