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SUMMARYThis paper presents a convection-di usion-reaction (CDR) model for solving magnetic induction equations and incompressible Navier-Stokes equations. For purposes of increasing the prediction accuracy, the general solution to the one-dimensional constant-coe cient CDR equation is employed. For purposes of extending this discrete formulation to two-dimensional analysis, the alternating direction implicit solution algorithm is applied. Numerical tests that are amenable to analytic solutions were performed in order to validate the proposed scheme. Results show good agreement with the analytic solutions and high rate of convergence. Like many magnetohydrodynamic studies, the Hartmann-Poiseuille problem is considered as a benchmark test to validate the code.

Remnant livers will be regenerated in live donors after a large volume resection for transplantation. How the structures and hemodynamics of portal vein will evolve with liver regeneration remains unknown. This prompts the present hemodynamic simulation for a 25 year-old man who received a right donor lobectomy. According to the magnetic resonance imaging/computed tomography images taken prior to the operation and one month after the operation, three sequential models of portal veins (pre-op, immediately after the operation, and one-month post-op) were constructed by AMIRA and HYPERMESH, while the immediately after the operation model was generated by removing the right branch in the pre-op model. Hemodynamic equations were solved subject to the sonographically measured inlet velocity. The simulated branch velocities were compared with the measured ones. The predicted overall pressure in the portal vein after resection was found to increase to a magnitude that has not reached to an extent possibly leading to portal hypertension. As expected, blood pressure has a large change only in the vicinity of the resection region. The branches grew considerably different from the original one as the liver is regenerated. Results provide useful evidence to justify the current computer simulation.

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SUMMARYA nodally exact convection-diffusion-reaction scheme developed in Cartesian grids is applied to solve the flow equations in irregular domains within the framework of immersed boundary (IB) method. The artificial momentum forcing term applied at certain points in the flow and inside the body of any shape allows the imposition of no-slip velocity condition to account for the body of complex boundary. Development of an interpolation scheme that can accurately lead to no-slip velocity condition along the IB is essential since Cartesian grid lines generally do not coincide with the IB. The results simulated from the proposed IB method agree well with other numerical and experimental results for several chosen benchmark problems. The accuracy and fidelity of the IB flow solver to predict flows with irregular IBs are therefore demonstrated.