TY - JOUR
T1 - Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow
AU - Neda, Monika
AU - Pahlevani, Faranak
AU - Rebholz, Leo G.
AU - Waters, Jiajia
N1 - Funding Information:
The work of the third author was partially supported by NSF grant DMS1112593.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and nonisothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.
AB - We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and nonisothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.
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U2 - 10.1515/jnma-2015-1017
DO - 10.1515/jnma-2015-1017
M3 - Article
AN - SCOPUS:84990872937
SN - 1570-2820
VL - 24
SP - 189
EP - 206
JO - Journal of Numerical Mathematics
JF - Journal of Numerical Mathematics
IS - 3
ER -