Embedded boundary / cut cell methods are one approach to solving the equations for fluid flow in the presence of complex geometries. In the cut cell approach, the boundary of the domain is treated as an interface in a (locally) uniform background mesh, resulting in grid cells that are of uniform size and shape away from the interface, but irregular and potentially very small immediately adjacent to the surface. The “small cell problem” refers to the algorithmic challenge that results from standard discretization approaches on very small cut cells.
State redistribution (SRD) is one approach to addressing the small cell problem. Like the classic flux redistribution approach, state redistribution modifies the advective update in and near small cut cells to enforce numerical stability. In the original formulation by Berger and Guiliani (2020), state redistribution was applied to compressible flow in two dimensions. In more recent work, we have extended the SRD algorithm to three dimensions, generalized it using a less dissipative weighting scheme, and applied it to low Mach number flows. An open-source performance-portable software implementation of SRD in two and three dimensions is now available.
In this talk we present the weighted state redistribution algorithm and contrast results with the flux redistribution scheme. We illustrate the use of the method in compressible combustion and incompressible flow applications and discuss possible further extensions of the algorithm.
About the speaker
Dr Ann Almgren is a Senior Scientist and the Department Head of the Applied Mathematics Department in the Applied Mathematics and Computational Research Division at Lawrence Berkeley National Laboratory. Her primary research interest is in computational algorithms for solving PDEs in a variety of application areas. Her current projects include the development and implementation of new multiphysics algorithms in high-resolution adaptive mesh codes that are designed for the latest hybrid architectures.
She is a SIAM Fellow, the Deputy Director of the ECP AMReX Co-Design Center, and serves on the editorial boards of CAMCoS and IJHPCA. Prior to coming to LBL she worked at the Institute for Advanced Study in Princeton, NJ, and at Lawrence Livermore National Lab.
Monday 6 March
11:00 – 12:00
JJ Thomson seminar room
JJ Tomson Ave, Cambridge
Or join us on Zoom:
Meeting ID: 835 5747 5574
Find your local number: https://us06web.zoom.us/u/kdmQtIKdbI
Monday, 6 March, 2023 – 11:00 to 12:00
Hybrid – Maxwell Centre, Cambridge & on Zoom