We present a robust, highly accurate, and efficient positivity- boundedness-preserving diffuse interface method for the simulations of compressible gas-liquid two-phase flows with five-equation model by Allaire et al. using high-order finite difference weighted compact nonlinear scheme (WCNS) in explicit form. The equation states gas liquid are given ideal stiffened laws respectively. Under mil...

We present an a posteriori shock-capturing finite volume method algorithm called GP-MOOD that solves compressible hyperbolic conservative system at high-order solution accuracy (e.g., third-, fifth-, and seventh-order) in multiple spatial dimensions. The combines two methodologies, the polynomial-free reconstruction methods of GP (Gaussian Process) detection algorithms MOOD (Multidimensional Op...

We consider complex scenarios involving two-way coupled interactions between compressible fluids and solid bodies under extreme conditions where monolithic, as opposed to partitioned, schemes are preferred for maintaining stability. When considering such problems, spurious numerical cavitation can be quite common and have deleterious consequences on the flow field stability, accuracy, etc. Thus...

In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with detailed balance condition. The is constructed based on recently developed energetic variational formulation, in which reaction part reformulated terms trajectories. fact that both diffusion parts dissipate same free open...