Reduced Blood Flow Models: Numerical Methods and Applications

In this talk, we present several mathematical models for reduced blood flow in compliant vessels that arise as systems of nonlinear hyperbolic conservation laws in one space dimension. Their simplicity allows for efficient simulation of blood flow in complex networks of vessels representing the arterial and venous trees. We describe discontinuous Galerkin and characteristics-based discretizations for simulating these equations, compare and contrast these methods with numerical results, and discuss their relative advantages / disadvantages. Lastly, we discuss future work in applying these equations to study the complex physiology of congenital heart defects.

Speaker Bio: Charles is currently a fourth year Ph.D. student in the Department of Computational and Applied Mathematics at Rice University under the supervision of Beatrice Riviere. His current research interests include numerical partial differential equations with application to cardiovascular mathematics, modeling and clinical decision support. He earned his B.A. in mathematics and physics from Wesleyan University in 2011 and his M.A. from Rice University in 2013 under the direction of Mark Embree. His masters work focused on large-scale eigenvalue computations and spectral theory for mathematical models of quasicrystals.

Note: Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.