## IMA Postdoc Seminar (December 2, 2008)

**Speaker:** Yunkyong Hyon (IMA)

**Title:** Maximum Dissipation Principle for Numerical Methods in Complex
Fluids

**Abstract:** We discuss the general energetic variational approaches for
hydrodynamic systems of complex fluids. In these energetic variational
approaches, the least action principle (LAP) with action functional
gives the Hamiltonian parts (conservative force) of the hydrodynamic
systems, and the maximum/minimum dissipation principle (MDP), i.e.,
Onsager's principle, gives the dissipative parts (dissipative force) of
the systems. When we combine the two systems derived from the two
different principles, we obtain a whole coupled nonlinear system of
equations satisfying the dissipative energy laws. We will discuss the
important roles of MDP in designing numerical method for computations of
hydrodynamic system in complex fluids. We will reformulate the
dissipation in energy equation in terms of a rate in time by using an
appropriate evolution equations, then the MDP is employed in the
reformulated dissipation to obtain the dissipative force for the
hydrodynamic system. The systems are consistent with the Hamiltonian
parts which are derived from LAP. This procedure allows the usage of
lower order element (a continuous $C^0$ finite element) in numerical
method to solve the system rather than high order elements, and at the
same time preserves the dissipative energy law.

**Slides:** PDF