9,167 research outputs found
A bounded upwinding scheme for computing convection-dominated transport problems
A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data
High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
The paper develops high-order accurate physical-constraints-preserving finite
difference WENO schemes for special relativistic hydrodynamical (RHD)
equations, built on the local Lax-Friedrich splitting, the WENO reconstruction,
the physical-constraints-preserving flux limiter, and the high-order strong
stability preserving time discretization. They are extensions of the
positivity-preserving finite difference WENO schemes for the non-relativistic
Euler equations. However, developing physical-constraints-preserving methods
for the RHD system becomes much more difficult than the non-relativistic case
because of the strongly coupling between the RHD equations, no explicit
expressions of the primitive variables and the flux vectors, in terms of the
conservative vector, and one more physical constraint for the fluid velocity in
addition to the positivity of the rest-mass density and the pressure. The key
is to prove the convexity and other properties of the admissible state set and
discover a concave function with respect to the conservative vector replacing
the pressure which is an important ingredient to enforce the
positivity-preserving property for the non-relativistic case. Several one- and
two-dimensional numerical examples are used to demonstrate accuracy,
robustness, and effectiveness of the proposed physical-constraints-preserving
schemes in solving RHD problems with large Lorentz factor, or strong
discontinuities, or low rest-mass density or pressure etc.Comment: 39 pages, 13 figure
Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations
This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook)
schemes in the framework of finite volume method for the ultra-relativistic
flows. Different from the existing kinetic flux-vector splitting (KFVS) or
BGK-type schemes for the ultra-relativistic Euler equations, the present
genuine BGK schemes are derived from the analytical solution of the
Anderson-Witting model, which is given for the first time and includes the
"genuine" particle collisions in the gas transport process. The BGK schemes for
the ultra-relativistic viscous flows are also developed and two examples of
ultra-relativistic viscous flow are designed. Several 1D and 2D numerical
experiments are conducted to demonstrate that the proposed BGK schemes not only
are accurate and stable in simulating ultra-relativistic inviscid and viscous
flows, but also have higher resolution at the contact discontinuity than the
KFVS or BGK-type schemes.Comment: 41 pages, 13 figure
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