Viscous fluids, elasticity and function-theory. I

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...

Lattice-Gas Dynamics, Volume I Viscous Fluids

Lattice-Gas Dynamics Volume I Viscous Fluids The theory and computation of lattice gas dynamics for viscous fluid hydrodynamics is presented. Theoretical analysis of these exactly conserved, discrete models is done using the Boltzmann approximation, a mean-field theoretical treatment. Theoretical results are then compared to numerical data arrived at by exactly computed simulations of simple la...

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

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...