Portal hypertension is one of the major complications in patients with chronic liver diseases (CLD) which induces the increase in portal vein gradient pressure. At advanced stage, it can cause the esophageal varices and variceal hemorrhage. Therefore, portal hypertension has been the leading cause of mortality in CLD patients. To diagnose portal hypertension, the invasive hepatic venous pressure gradient (HVPG) measurement is still the only validated technique to accurately evaluate changes in portal pressure and regarded as the standard reference. However, it entails the limitation of invasive procedure and have the risk of further bleeding and inflammation. In this paper we propose an Eulerian computational fluid dynamics (CFD) model to facilitate hemodynamics analysis. To enable consistent simulation results with different boundary conditions, a diffuse boundary handling technique was proposed to impose smooth boundary conditions for both the pressure and velocity fields. We also propose a computational workflow for quantifying patient-specific hemodynamics in portal vein systems non-invasively. The simulation is performed on patient-specific PV models reconstructed from CT angiographic images. Experiments show that pressure changes in the PV of patients with portal hypertension due to blockage of the RPV are significantly lower than that of normal subjects.