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.
Highlights
Smoothed Particle Hydrodynamics (SPH) is a widely used mesh-free method for Computational Fluid Dynamics
We have presented a new high-accurate SPH-Arbitrary Lagrangian–Eulerian (ALE) method for weakly compressible flow, which can deal with discontinuities
A new approach to compute the viscous flows terms is presented, where Moving Least Squares approximations are used to increase the accuracy and compute the derivatives needed for viscous fluxes
Summary
Smoothed Particle Hydrodynamics (SPH) is a widely used mesh-free method for Computational Fluid Dynamics. The incompressibility is approximated by artificially allowing a slight flow compressibility One advantage of this approach is that it avoids the need for solving a Poisson equation to compute the pressure field. The second procedure is more recent, and was introduced by Marrone et al [13] They developed the δ-SPH scheme, in which a density diffusive term is added to smooth the spurious density oscillations. Among the a priori approaches we can name limiting or stabilizing procedures used in SPH such as artificial viscosity [16,17], MUSCL with slope limiter [18], or ENO/WENO [19,20] These methods are applied to locally increase the numerical diffusion for eliminating the nonphysical oscillations. This approach does not increase the computational complexity of the scheme since the viscous terms are computed using the same reconstruction already calculated for the convective terms
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
