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Advanced Numerical Methods in the Mathematical Sciences

Charles Puelz, Rice University
Discontinuous Galerkin Methods for Reduced Blood Flow Models


In this work, we present several models of reduced, one-dimensional blood flow through compliant vessels that are formulated as systems of nonlinear hyperbolic conservation laws. We describe several discontinuous Galerkin formulations for the spatial discretization of the models, and discuss approaches for modeling networks of vessels. Numerical results comparing different models and discretizations are presented. Lastly, we discuss the application of these models in the study of the complex physiology of patients impacted by congenital heart defects.