We present a high performance computing framework for finite element simulation of blood flow in the left ventricle of the human heart. The mathematical model is described together with the discretization method and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. We show results based on patient-specific data that capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several other studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.