Ju Liu's blog

Solving incompressible elasticity has been quite challenging numerically. The conventional approach for handling incompressibility is the so-called penalty method. A volumetric energy term enters into the strain energy and penalizes the volumetric deformation. One straightforward issue is that the penalty parameter goes directly into the tangent matrix. The bigger the penalty parameter, the worse the condition number of the matrix. This is really a manifestation of the ill-posedness of theories based on the Helmholtz free energy, in my opinion [3].

In our recent work, we have developed a thermomechanical theory for multiphase flows, wich particular focus on the van der Waals fluid. By invoking Gurtin's microforce theory, the Coleman-Noll approach is generalized to derive constitutive relations in the presence of non-local effects. A new fully discrete numerical scheme for the model problem is designed. The scheme is provably unconditionally stable in entropy and second-order accurate in time. Using these technologies, the liquid-vapor boiling problem is investigated.