Development of algorithms
for convection-dominated problems under compressible
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 algebraic

constraints 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.

Implementation
and testing of the proposed algorithm

Applied
mathematics and computational science