A compressible multi-fluid scheme based on upwind space-time Conservation Element and Solution Element method and its application to underwater detonation jet

The underwater detonation jet provides an efficient means of generating pulsating bubbles by igniting a detonation tube underwater. For simulating the transient detonation jet phenomenon involving three kinds of fluid, i.e., air, water and detonation gas, we develop in this paper a compressible multi-fluid scheme, which can well capture the shock propagation and bubble dynamics. The scheme is based on the upwind space-time Conservation Element and Solution Element (CE/SE) method, which solves the volume fraction-based Allaire-Massoni model on staggered quadrilateral meshes with all fluids following the stiffened gas law. The upwind scheme is adopted in the evaluation of numerical flux through interior boundaries inside each CE. To satisfy the maximum principle during the calculation, a slope limiter is specifically constructed and applied to volume fractions, partial densities and mixture density to ensure their boundedness-preserving requirements. To validate the robustness and accuracy of the solver, several benchmark cases are carried out, and the simulated results are compared with the corresponding theoretical or experimental data. Finally, we apply the scheme to simulate the pulse jet process of a detonation tube ignited underwater. The simulated results agree well with the previous experimental data, in terms of the bubble morphology and equivalent radius.