STOKES (BACK)

STOKES

The Stokes code simulates stationary flows for Newtonian fluids in a given meshed cavity. A mixed finite element method of type (P1+/P1) is used (i.e. continuous interpolations for pressure and velocity at the nodes). There are 4 unknowns (Vx, Vy, Vz and P) for each node in a 3D case, and 3 unknowns (Vx, Vy and P) in a 2D case. Once assembled, the global matrix is pre-conditioned by PETSc using ILU(0). Then, PETSc solves the linear system using a conjugate residual method. The meshed cavity is partitioned, then each processor computes the flow inside its own part of the cavity. Communications between processors mostly happens at the interfaces of the partition (i.e. at the nodes that belong to several processors).

Results on the "mecagrid" grid :
Extrusion

This example is is a 3D extrusion of a profile. The Figure illustrates the result of extrusion on th 65.000 vertice mesh. The table 6 shows the results for 65.000 vertices mesh. The second one 7 shows results for 500.000 vertices mesh. Poor performances of inter-cluster communications are visible in these tables and make necessary to use more larger tests.

Table 6: 65.000 vertices example
Used clusters INRIA IUSTI CEMEF INRIA-CEMEF-IUSTI
Number of processors 3 3 3 3 (1-1-1) 9 (3-3-3)
Number of iterations 653 650 653 651
657
Total simulation time(s) 87.56 173.66 455.57 649.52 495.37

 

Table 7: 500.000 vertices example
Used clusters INRIA IUSTI CEMEF INRIA-CEMEF-IUSTI
Number of processors 6 6 6 6 (2-2-2)
Number of iterations 1075 1069 1069 651
Total simulation time(s) 692.78 1903.78 1357.1 2995.01

 

Bibliographical references :