Abstract:

When the complex evolution of multi-physics systems is treated as a monolithic object, the time step selection is governed by the most rapidly varying component. However, the appropriate analysis can often reveal a splitting that allows rapid, efficient, and accurate simulation of the full system, by carefully coordinating the uncoupled computation of each subsystem.

We have developed numerical methods that address these important practical problems: modular use of existing sub-physics legacy codes and integration of uncertainty quantification techniques in legacy codes. We have examined the novel decoupling techniques using both rigorous analytic mathematical theory and relevant numerical experiments.

I will illustrate these ideas with specific examples: the implicit-explicit approach for uncoupling evolution equations with exact skew-symmetric coupling, in fluid-structure interaction and the equations for magneto-hydrodynamic fluid flow

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