Coloquio Queretano de Matemáticas

Resumen:

In the first part, we formulate a one dimensional isothermal drift flux model of two phase
flows which is fully hyperbolic and conservative. The exact solution of this system,
consisting of elementary waves has been derived. Furthermore, using the singular surface
theory the evolution of discontinuity is discussed. In the second part, we formulate a
weakly compressible two-layer shallow water flow in channels with arbitrary cross
sections. This model is a balance law with non-conservative products. Using the method
of generalised Rankine-Hugoniot conditions we derive the Riemann invariants for the
shock and contact wave. Furthermore, a high-resolution, non-oscillatory semi-discrete
central-upwind scheme is presented. The scheme extends existing central-upwind semi
-discrete numerical methods for hyperbolic balance laws. We validate the exact solution
with the numerical approach.