Simulation of Counter-Current Spontaneous Imbibition Based on Momentum Equations with Viscous Coupling, Brinkman Terms and Compressible Fluids

Heat Convection of Compressible Viscous Fluids. I

The stationary problem for the heat convection of compressible fluid is considered around the equilibrium solution with the external forces in the horizontal strip domain z0 < z < z0 + 1 and it is proved that the solution exists uniformly with respect to z0 ≥ Z0 . The limit system as z0 → +∞ is the Oberbeck-Boussinesq equations. Mathematics Subject Classification (2010). Primary 35Q35; Secondar...

Mathematical theory of compressible, viscous, and heat conducting fluids

We review some recent results on the Navier–Stokes–Fourier system governing the evolution of a general compressible, viscous, and heat conducting fluid. We discuss several concepts of weak solutions, in particular, using the implications of the Second law of thermodynamics. We introduce the concept of relative entropy and dissipative solution and show the principle of weak-strong uniqueness. We...

Problems in the Theory of Viscous Compressible Fluids

On the Navier-stokes Equations for Exothermically Reacting Compressible Fluids

We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, includin...

Fast simulation of viscous fluids with elasticity and thermal conductivity using position-based dynamics

Viscous fluids are ubiquitous, and reproducing their damped motions has been in demand for many applications. The most prevalent approach to simulating viscous fluids is based on the Navier-Stokes equations and necessitates viscosity integration. However, to simulate viscous fluids in a numerically stable manner, using explicit viscosity integration severely restricts time steps and requires an...