A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms

TL;DR

This paper introduces a kinetic numerical scheme for modeling unsteady mixed flows in non-uniform closed pipes, effectively handling complex source terms related to topography, section variation, curvature, and friction within a finite volume framework.

Contribution

It proposes a novel kinetic upwind approach that incorporates source terms directly into fluxes, improving the accuracy of mixed flow simulations in complex pipe geometries.

Findings

The scheme accurately captures transient mixed flows.

Numerical tests validate the effectiveness of the approach.

The method handles complex source terms without loss of stability.

Abstract

We present a numerical kinetic scheme for an unsteady mixed pressurised and free surface model. This model has a source term depending on both the space variable and the unknown, U, of the system. The source term is composed by a topography, a section variation, a curvature (also called corrective) and a friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose an approximation of the source terms following the principle of interfacial upwind with a kinetic interpretation: the source term is not treated as a volumic term, but included in the numerical fluxes. Then, several numerical tests are presented.