Fully adaptive and integrated numerical methods for the simulation and control of variable density multiphase flows governed by diffuse interface models.

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In this project we (a) develop and analyse numerical methods for the simulation of multiphase flow problems with variable fluid densities which guarantee a locally refined resolution of the local processes at the interface; (a') propose adaptive discretization concepts for the coupling of diffuse interface models and surface partial differential equations (PDEs); (b) develop, implement and analyze model-predictive feedback control strategies for multiphase flows governed by diffuse interface models; (c) formulate and analyze optimal control problems for multiphase flows; (d) develop robust and reliable solution strategies for optimal control of multiphase flows governed by diffuse interface models. The primary focus of our work is on (a) and (a'), where as the topics (b)--(d) are to be developed subsequently based on the results achieved in (a), (a') and given the expertise of the applicants in the development of algorithms and discretization techniques for optimal control of partial differential equations and variational inequalities including the CHNS system.