In cardiovascular mechanics, reaching consensus in simulation results within a physiologically relevant range of parameters is essential for reproducibility purposes. Although currently available benchmarks contain some of the features that cardiac mechanics models typically include, some important modeling aspects are missing. Therefore, we propose a new set of cardiac benchmark problems and solutions for assessing passive and active material behavior, viscous effects, and pericardial boundary condition. The problems proposed include simplified analytical fiber definitions and active stress models on a monoventricular and biventricular domains, allowing straightforward testing and validation with already developed solvers.

We present a loosely-coupled approach for the solution of the thermo-fluid-structure interaction problem, based on Dirichlet-Neumann partitioning. A cartesian grid finite volume scheme, with conservative interface method is used for the fluid and a finite-element scheme for the thermo-structure problem. Special attention is given to the transfer of forces, temperatures and to the structural positions. The structural surface is represented by a level set function in the fluid code. The velocity and temperature field required for the coupling are interpolated from structural values on the zero-contour level set surface. Data transfer between the two codes is performed via message passing interface. The proposed method is tested for a cooling-process of a heated metal bar by mean of an external laminar boundary layer flow. Results show that the presented approach is able to handle the complexity of the three-field problem.