We apply a recent extension of the Hele-Shaw scheme to analyze steady compressible viscous flows through micro T-junctions. The linearity of the problem in terms of an appropriately defined quadratic form of the pressure facilitates the definition of the viscous resistance of the configuration, relating the gas mass-flow rate to entrance and exit conditions. Furthermore, under rather mild restr...

The evolution of an inertial fusion energy (IFE) chamber involves a repetition of short, intense depositions of energy (from target ignition) into a reaction chamber, followed by the turbulent relaxation of that energy through shock waves and thermal conduction to the vessel walls. We present an algorithm for 2D simulations of the fluid inside an IFE chamber between fueling repetitions. Our fin...

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature the proposed algorithm is efficient via derivative sharing between inviscid viscous schemes: highly accurate explicit implicit gradients are used solution expressed in terms derivatives. higher-order velocity components reused to comput...

In the present study, a discontinuous Galerkin (DG) framework is developed to simulate chemically reacting flows. The algorithm combines a double-flux method to account for variable thermodynamic properties, a Strang-splitting scheme for the stiff reaction chemistry, a robust WENO-based shock limiter, and the non-linear viscous-diffusive transport is discretized using the BR2 method. The algori...

A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant γ ∈ [1, 3). This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound uniformly away from cavitation for the viscous approximate velocity fields. Mathematical entropy pairs...

Abstract. The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space R and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a d...

Potential flows u = ∇φ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term μ∇u = μ∇∇φ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers e...