A Finite-Volume/Newton Method for a Two-Phase Heat Flow Problem Using Primitive Variables and Collocated Grids
✍ Scribed by M.C. Liang; C.W. Lan
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 516 KB
- Volume
- 127
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
staggered grids [8]. The major drawback in these schemes is from the staggered grid allocation. Using different grids A finite-volume/Newton's method is presented for solving the incompressible heat flow problem in an inclined enclosure with an for different variables has made the staggered grid apunknown melt/solid interface using primitive variables and colloproach less attractive to the problems with complex twocated grids. The unknown melt/solid interface is solved simultaneand three-dimensional geometries and free boundaries [9].
ously with all of the field variables by imposing the weighted melt-
The same is true to use the staggered grids in multigrid ing-point isotherm. In the finite-volume formulation of the continuity implementation. An additional drawback is the slow conequation, a modified momentum interpolation scheme is adopted to enhance velocity/pressure coupling. During Newton's iterations, vergent speed of the SIMPLE iterations, and its convergent the ILU (0) preconditioned GMRES matrix solver is applied to solve speed is often mesh dependent. To amend this, Newton's the linear system, where the sparse Jacobian matrix is estimated method could be used (e.g., Refs. [10, 13]). Although the by finite differences. Nearly quadratic convergence of the method convergence rate of Newton's method is quadratic and is observed. The robustness of the method is further enhanced with the implementation of the pseudo-arclength continuation. The independent of the grid number used [10], complicated effects of the Rayleigh number and gravity orientation on flow pat-Jacobian matrices need to be estimated, and the computer terns and the interface are demonstrated. Bifurcation diagrams are memory required for the solution of Newton's linear equaalso constructed to illustrate flow transition and multiple steady tions is much larger. Nevertheless, Newton-like approaches states.