Iterative algorithms for scalar conservation laws and volume of fluids


Project Description

Development of algorithms for convection-dominated problemsundercompressible flows is an important topic for applications like sediment transport.If the transport of a quantity saturates then the solution of the transport equations must be bounded by physical constraints. This process could in principle be modeled via the constitutive relations of the flow model. Alternatively, one could impose algebraicconstraints in the transport solver to guarantee the physical bounds.With this project we aim to review recent methods for solving transport equations (under compressible flows) that impose physically motivated bounds on the solution.In addition, we are interested on exploring novel methodologies based on flux correctionfor continuous Galerkin finite elements to achieve the desired goals.​​
Program - Applied Mathematics and Computer Science
Division - Computer, Electrical and Mathematical Sciences and Engineering
Field of Study - ​Applied mathematics and computational science

About the

David I. Ketcheson

Associate Professor, Applied Mathematics and Computational Science

David I. Ketcheson

​Professor Ketcheson's research interests are in the areas of numerical
analysis and hyperbolic PDEs. His work includes development of efficient
time integration methods, wave propagation algorithms, and modeling of
wave phenomena in heterogeneous media.

Desired Project Deliverables

​Implementation and testing of the proposed algorithm​