■The development of numerical methods for the solution of complex problems in engineering and science, mostly at the continuum scale.
■Complex rheology: multiscale and continuum methods for incompressible viscoelastic flows.
■Multiphase flows: compressible and incompressible flows of fluids and elastic-plastic solids in time-dependent domains, interfacial processes.
■Constitutive modeling: equations of state, thermodynamic modeling, symmetry invariants.
■Charged systems: plasma physics, boundary charge and bilayer problems