An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows
(2017) Computational Science Engineering (CSE17) — Location: Atlanta (27.February.2017)
Files
Penalization_CSE17.pdf
Open Access - Adobe PDF
- 2.82 MB
Details
- Authors
Gillis, Thomas 
- Abstract
- The Vortex Particle-Mesh (VPM) method is well suited for solving advection dominated incompressible flows. However, the efficient and accurate handling of solid boundaries in this method is still an active domain of research. The Brinkman penalization method embeds the object in the fluid domain and en- forces the velocity inside the obstacle to be u = ub, where ub is the desired velocity. This additional constraint is added to the vorticity form of the incom- pressible Navier-Stokes equations through a Lagrange relaxation. The boundary enforcement conditions the capture of vorticity production at the wall and is thus paramount to the accuracy of the global method. Hejlesen et al. proposed to first solve the unpenalized Navier-Stokes equations and then, to impose the constraint using a Jacobi-like iterative process. In this work, we formulate the penalization problem inside a VPM method as a linear system to solve at every time step. Recovering the velocity from the vorticity (i.e. solving a Poisson problem) makes the matrix-vector product highly expensive. We use a recy- cling iterative solver, rBiCGStab, to solve it in order to reduce the number of iterations. This method is validated against a benchmark flow past a cylin- der (Re = 550) and then, we assess the computational gain with a flow past a cylinder and a plate (Re = 9500 and Re = 1000, respectively).
- Affiliations
Citations
Gillis, T., Winckelmans, G., & Chatelain, P. (2017). An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows. Computational Science Engineering (CSE17), Atlanta. https://hdl.handle.net/2078.5/221272