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Title: A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

Journal Article · · SIAM Journal on Scientific Computing
DOI: https://doi.org/10.1137/22m1532019 · OSTI ID:2325975
 [1];  [2];  [2];  [1];  [1];  [1]
  1. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
  2. Colorado State Univ., Fort Collins, CO (United States)
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A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
2325975
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 45; ISSN 1064-8275
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

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97 MATHEMATICS AND COMPUTING
high-order finite volume
embedded boundary
Stokes equations