In this work, parallel solution of the Navier-Stokes equations for a mixed convection heat problem is achieved using a finite-element-based finite-volume method in fully coupled and semi coupled algorithms. A major drawback with the implicit methods is the need for solving the huge set of linear algebraic equations in large scale problems. The current parallel computation is developed on distributed memory machines. The matrix decomposition and solution are carried out using PETSc library. In the fully coupled algorithm, there is a 36-diagonal global matrix for the two-dimensional governing equations. In order to reduce the computational time, the matrix is suitably broken in several sub-matrices and they are subsequently solved in a segregated manner. This approach results in four 9-diagonal matrices. Different sparse solver algorithms are utilized to solve a mixed natural-forced convection problem using either fully-coupled or semi-coupled algorithms. The performance of the solvers are then investigated in solving on a distributed computing environment. The study shows that the iteration run time considerably decreases although the overall run time of the fully coupled algorithm still looks better.

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