THOMAS HOU
Applied Math, 217-50
Caltech
Pasadena, CA 91125
hou@ama.caltech.edu
Abstract:
We develop an efficient dynamically adaptive mesh generator for time-dependent problems in two or more dimensions. The mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic PDEs for the mesh map. When the mesh map is coupled to a physical problem, it evolves with the physical solution and maintains high adaptivity as the solution develops complicated structures. Our mesh strategy is simple to implement, avoids interpolation, and it gives the best performance when the physical solution is nearly singular. The new dynamic mesh generator can be easily incorporated into a broad range of applications in multidimensional problems. Here we apply it to investigate the baroclinic generation of vorticity in a strongly layered two-dimensional Boussinesq fluid. The adaptive mesh follows effectively the flow resolving the almost singular shear layers developed dynamically. The numerical results show the fast collapse to small scales and an exponential vorticity growth.