Open AccessA Numerical Study of a Modular Sparse Grad-Div Stabilization Method for Boussinesq Equations
Author(s) -
Medine Demir,
Songül Kaya
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1391/1/012097
Subject(s) - modular design , block (permutation group theory) , stability (learning theory) , mathematics , computer science , mathematical optimization , geometry , operating system , machine learning
This study presents a modular sparse grad-div stabilization method for solving the Boussinesq equations. Unlike the usual grad-div stabilization which produces fully coupled block matrices, the proposed stabilization method produces block upper triangular matrices. Thus, the proposed method is more attractive in terms of both its computational cost and solution accuracy. We provide unconditional stability results for velocity and temperature. Two numerical experiments are performed to demonstrate the efficiency and accuracy of the method.