WELL-BALANCED ROE-TYPE NUMERICAL SCHEME FOR A MODEL OF TWO-PHASE COMPRESSIBLE FLOWS

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

A Roe-type Scheme for Two-phase Shallow Granular Flows over Variable Topography

We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid component...

Numerical Simulation of Compressible Two-phase Flows Using an Eulerian Type Reduced Model

Computing compressible two-phase flows that consider different materials and physical properties is conducted. A finite volume numerical method based on Godunov approach is developed and implemented to solve an Euler type mathematical model. This model consists of five partial differential equations in one space dimension and it is known as the reduced model. A fixed Eulerian mesh is considered...

Compressible Two-Phase Flows: Two-Pressure Models and Numerical Methods

A conservative hyperbolic model for compressible two-phase two-fluid model is studied and numerical methods for its approximate solution are proposed. The derivation of the governing equations of the model is based on the principles of extended thermodynamics. The field equations form a hyperbolic system of balance equations in conservative form, which guarantees the well-posedness of the initi...

Central Upwind Scheme for a Compressible Two-Phase Flow Model

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side whi...