Advances in Moving Mesh Methods
Abstract:
To solve time-dependent PDEs numerically, a method of lines approach is typically implemented; the PDE is discretized in space with an appropriate spatial mesh, and the resulting system of DAEs are integrated using a suitable time-integrator. It is often advantageous to employ an adaptive spatial mesh if fine-scale structures propagate, dissipate, or develop as the solution evolves. Examples of such behaviors are observed in combustion simulations as well as shock formation in fluid flows. In this talk, we will discuss some recent advances in moving mesh methods (the so-called r-adaptive methods), which allow for the natural addition or removal of grid nodes.
Applied Mathematics Seminar