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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

References (24)

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators
  • Khalili, M. Ehsan; Larsson, Martin; Müller, Bernhard
  • International Journal for Numerical Methods in Fluids, Vol. 89, Issue 7 https://doi.org/10.1002/fld.4696
journal December 2018
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains journal November 1998
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries book January 1997
Numerical analysis of blood flow in the heart journal November 1977
A second-order projection method for the incompressible navier-stokes equations journal December 1989
Additive Runge–Kutta schemes for convection–diffusion–reaction equations journal January 2003
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations journal November 1997
A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement journal December 2015
A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions journal January 2008
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics journal January 2008
High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids journal May 2015
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I journal September 2017
Analytical model for the prediction of permeability of triply periodic minimal surfaces journal December 2021
Numerical simulation of incompressible viscous flow in deforming domains journal May 1999
Embedded boundary grid generation using the divergence theorem, implicit functions, and constructive solid geometry journal July 2008
Numerical solution of the Navier-Stokes equations journal January 1968
A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation journal January 2012
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems journal September 2005
Immersed Boundary Methods journal January 2005
A high-order finite-volume method for conservation laws on locally refined grids journal January 2011
A cartesian grid embedded boundary method for the compressible Navier–Stokes equations journal January 2013
An adaptive finite volume method for the incompressible Navier–Stokes equations in complex geometries journal January 2015
A fourth-order Cartesian grid embedded boundary method for Poisson’s equation journal January 2017
Towards a High-Order Embedded Boundary Finite Volume Method for the Incompressible Navier-Stokes Equations with Complex Geometries conference January 2022

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Related Subjects

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