A Divergence-Free Multidomain Spectral Solver of the Navier–Stokes Equations in Geometries of High Aspect Ratio

1998 ◽  
Vol 139 (2) ◽  
pp. 359-379 ◽  
Author(s):  
C. Sabbah ◽  
R. Pasquetti
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Divergence Free

Hierarchical Divergence-Free Bases and Their Application to Particulate Flows

2003 ◽  
Vol 70 (1) ◽  
pp. 44-49 ◽  
Author(s):  
V. Sarin ◽  
A. H. Sameh
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Particulate Flow ◽  
Particulate Flows ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Rigid Particles ◽  
The Matrix ◽  
Divergence Free

The paper presents an algebraic scheme to construct hierarchical divergence-free basis for velocity in incompressible fluids. A reduced system of equations is solved in the corresponding subspace by an appropriate iterative method. The basis is constructed from the matrix representing the incompressibility constraints by computing algebraic decompositions of local constraint matrices. A recursive strategy leads to a hierarchical basis with desirable properties such as fast matrix-vector products, a well-conditioned reduced system, and efficient parallelization of the computation. The scheme has been extended to particulate flow problems in which the Navier-Stokes equations for fluid are coupled with equations of motion for rigid particles suspended in the fluid. Experimental results of particulate flow simulations have been reported for the SGI Origin 2000.

scholarly journals Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

1974 ◽  
Vol 65 (2) ◽  
pp. 231-246 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. H. Seinfeld
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Excellent Agreement ◽  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Cavity

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 ≤ Gr 2 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

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