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In the development of numerical algorithms for gas dynamics simulations, one faces two fundamental difficulties: the first is the formation of discontinuous fronts (even from smooth data), and the second is the development of a wide range of dynamically evolving and interacting spatio-temporal scales. In this talk, we will present a simple and general framework to deal with these two problems. For the former, we propose the so-called $C$-method, a novel nonlinear artificial viscosity stabilization technique. For the latter, we introduce a new multiscale framework, consisting of a fast adaptive mesh generator and coupled Arbitrary Lagrangian-Eulerian scheme, as well as a new interface model for contact discontinuities. A key feature of our methods is that the modifications are made at the level of the underlying PDEs, allowing the user to implement the numerical scheme of their choice. Numerical results will be presented to demonstrate the efficacy of the algorithms.

Pizza at 11:50