A staggered-projection Godunov-type method for the Baer-Nunziato two-phase model

TL;DR

This paper introduces a novel staggered-projection Godunov-type numerical scheme for the Baer-Nunziato two-phase model, effectively suppressing oscillations at porosity interfaces while accurately capturing discontinuities.

Contribution

It develops a staggered-projection scheme that maintains Riemann invariant continuity across porosity jumps, improving numerical stability and accuracy in two-phase flow simulations.

Findings

Reduces spurious oscillations near porosity interfaces

Accurately captures shocks and discontinuities

Ensures stability in two-phase flow simulations

Abstract

When describing the deflagration-to-detonation transition in solid granular explosives mixed with gaseous products of combustion, a well-developed two-phase mixture model is the compressible Baer-Nunziato (BN) model, containing solid and gas phases. If this model is numerically simulated by a conservative Godunov-type scheme, spurious oscillations are likely to generate from porosity interfaces, which may result from the average process of conservative variables that violates the continuity of Riemann invariants across porosity interfaces. In order to suppress the oscillations, this paper proposes a staggered-projection Godunov-type scheme over a fixed gas-solid staggered grid, by enforcing that solid contacts with porosity jumps are always inside gaseous grid cells and other discontinuities appear at gaseous cell interfaces. This scheme is based on a standard Godunov scheme for the Baer-Nunziato model on gaseous cells and guarantees the continuity of the Riemann invariants associated with the solid contact discontinuities across porosity jumps. While porosity interfaces are moving, a projection process fully takes into account the continuity of associated Riemann invariants and ensure that porosity jumps remain inside gaseous cells. This staggered-projection Godunov-type scheme is well-balanced with good numerical performance not only on suppressing spurious oscillations near porosity interfaces but also capturing strong discontinuities such as shocks.