TY - JOUR
T1 - Variational Multiscale immersed boundary method for incompressible turbulent flows
AU - Kang, Soonpil
AU - Masud, Arif
N1 - Funding Information:
This work was partially supported by National Science Foundation (NSF) grant NSF-DMS-16-20231 . Computing resources for the numerical tests were provided by the Teragrid/XSEDE Program under grant TG-DMS100004 . This support is gratefully acknowledged. Authors thank Sharbel Nashar for help in post-processing the results in Section 5 .
Funding Information:
Arif Masud reports that the financial support was provided by the National Science Foundation, USA.This work was partially supported by National Science Foundation (NSF) grant NSF-DMS-16-20231. Computing resources for the numerical tests were provided by the Teragrid/XSEDE Program under grant TG-DMS100004. This support is gratefully acknowledged. Authors thank Sharbel Nashar for help in post-processing the results in Section 5.
Funding Information:
Arif Masud reports that the financial support was provided by the National Science Foundation , USA.
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11/15
Y1 - 2022/11/15
N2 - This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on surfaces that are immersed in the stationary background discretizations. An interface stabilized form is developed by applying the Variational Multiscale Discontinuous Galerkin (VMDG) method at the immersed boundaries. The formulation is augmented with a variationally derived ghost-penalty type term. The weak form of the momentum balance equations is embedded with a residual-based turbulence model for incompressible turbulent flows. A significant contribution in this work is the variationally derived analytical expression for the Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions at the immersed boundary. In addition, the analytical expression for the interfacial stabilization tensor emerges which accounts for the geometric aspects of the cut elements that are produced when the immersed surface geometry traverses the underlying mesh. A unique attribute of the fine-scale variational equation is that it also yields a posteriori error estimator that can evaluate the local error in weak enforcement of the essential boundary conditions at the embedded boundaries. The method is shown to work with meshes comprised of hexahedral and tetrahedral elements. Numerical experiments show that the norm of the stabilization tensor varies spatially and temporally as a function of the flow physics at the embedded boundary. Test cases with increasing levels of complexity are presented to validate the method on benchmark problems of flows around cylindrical and spherical geometric shapes, and turbulent features of the flows are analyzed.
AB - This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on surfaces that are immersed in the stationary background discretizations. An interface stabilized form is developed by applying the Variational Multiscale Discontinuous Galerkin (VMDG) method at the immersed boundaries. The formulation is augmented with a variationally derived ghost-penalty type term. The weak form of the momentum balance equations is embedded with a residual-based turbulence model for incompressible turbulent flows. A significant contribution in this work is the variationally derived analytical expression for the Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions at the immersed boundary. In addition, the analytical expression for the interfacial stabilization tensor emerges which accounts for the geometric aspects of the cut elements that are produced when the immersed surface geometry traverses the underlying mesh. A unique attribute of the fine-scale variational equation is that it also yields a posteriori error estimator that can evaluate the local error in weak enforcement of the essential boundary conditions at the embedded boundaries. The method is shown to work with meshes comprised of hexahedral and tetrahedral elements. Numerical experiments show that the norm of the stabilization tensor varies spatially and temporally as a function of the flow physics at the embedded boundary. Test cases with increasing levels of complexity are presented to validate the method on benchmark problems of flows around cylindrical and spherical geometric shapes, and turbulent features of the flows are analyzed.
KW - Ghost penalty stabilization
KW - Immersed boundary method
KW - Large Eddy simulation
KW - Variational Multiscale (VMS) method
KW - Variational Multiscale Discontinuous Galerkin (VMDG) method
KW - Weakly imposed Dirichlet boundary conditions
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U2 - 10.1016/j.jcp.2022.111523
DO - 10.1016/j.jcp.2022.111523
M3 - Article
AN - SCOPUS:85138014938
SN - 0021-9991
VL - 469
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 111523
ER -