A bound-preserving oscillation-eliminating discontinuous Galerkin scheme for compressible two-phase flow
Provides a robust and efficient numerical method for simulating compressible two-phase flows with stiff source terms, addressing a key computational bottleneck for practitioners in computational fluid dynamics.
The paper develops a high-order bound-preserving oscillation-eliminating discontinuous Galerkin scheme for two-phase flows, overcoming the CFL restriction from stiff source terms via an operator-splitting strategy with unconditionally bound-preserving implicit time stepping. Numerical tests show superior robustness and efficiency.
This paper presents a high-order bound-preserving oscillation-eliminating discontinuous Galerkin (BP-OEDG) scheme for simulating gas-gas and gas-liquid two-phase flows governed by the Kapila five-equation model with the Tammann equation of state (EOS). The primary computational bottleneck arises from the severe CFL restriction imposed by the stiff $κ$-source term in the volume fraction equation. To circumvent this, we propose a novel operator-splitting strategy that decouples the system into a transport model and a stiff $κ$-source term. The former is discretized via a quasi-conservative DG method \cite{cheng2020quasi}, while the latter is resolved by an adaptive implicit strategy hybridizing the backward Euler and SDIRK2 methods. We rigorously prove that this implicit treatment is unconditionally BP, effectively removing the stiffness-induced stability constraints inherent in traditional explicit schemes. To further enhance precision, a velocity divergence reconstruction inspired by the Local Discontinuous Galerkin (LDG) method is integrated into the implicit solver. Furthermore, an OE limiter is employed to suppress spurious oscillations without characteristic decomposition, complemented by a BP limiter to ensure the BP property of partial densities, pressure, and volume fraction. Crucially, we prove that the proposed BP-OEDG scheme, integrated with the splitting strategy, strictly satisfies the Abgrall condition. Extensive numerical experiments, including challenging water-air shock-bubble interactions, demonstrate the superior robustness and efficiency of the method.