221 research outputs found
Convergence of a finite volume scheme for the compressible Navier--Stokes system
We study convergence of a finite volume scheme for the compressible
(barotropic) Navier--Stokes system. First we prove the energy stability and
consistency of the scheme and show that the numerical solutions generate a
dissipative measure-valued solution of the system. Then by the dissipative
measure-valued-strong uniqueness principle, we conclude the convergence of the
numerical solution to the strong solution as long as the latter exists.
Numerical experiments for standard benchmark tests support our theoretical
results.Comment: 21 pages, 2 figure
Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
We introduce dissipative solutions to the compressible Navier-Stokes system
with potential temperature transport motivated by the concept of Young
measures. We prove their global-in-time existence by means of convergence
analysis of a mixed finite element-finite volume method. If a classical
solution to the compressible Navier-Stokes system with potential temperature
transport exists, we prove the strong convergence of numerical solutions. Our
results hold for the full range of adiabatic indices including the physically
relevant cases in which the existence of global-in-time weak solutions is open
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