Related papers: Solving the Riemann Problem for Realistic Astrophy…
We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p =…
In the non viscous fluid dynamics, Smooth Particle Hydrodynamics (SPH), as a free Lagrangian "shock capturing" method adopts either an artificial viscosity contribution or an appropriate Riemann solver technique. An explicit or an implicit…
We present modifications to the Athena++ framework to enable use of general equations of state (EOS). Part of our motivation for doing so is to model transient astrophysics phenomena, as these types of events are often not well approximated…
This work considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…
In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…
An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid…
We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid…
The hard sphere system plays a basic role in condensed matter physics and related fields, and equation of state (EoS) is the ultimate solution to its thermodynamic properties (1-3). Dozens of EoSs have been proposed since van der Waals…
The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal…
The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the…
Godunov-type methods, which obtain numerical fluxes through local Riemann problems at cell interfaces, are among the most fundamental and widely used numerical methods in computational fluid dynamics. Exact Riemann solvers faithfully solve…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
Non-classical non-linear waves exist in dense gases for large specific heats at pressures and temperatures of the order of critical point values. These waves behave precisely opposite to the classical non-linear waves, with inverted…
The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in…
The Tolman VII solution (an exact static spherically symmetric perfect fluid solution) to the Einstein equations is reexamined, and a closed form equation of state (EOS) is deduced for the first time. This EOS allows further analysis…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
With the advance of supercomputers we can now afford simulations with very large ranges of scales. In astrophysical applications, e.g. simulating Solar, stellar and planetary atmospheres, interstellar medium, etc; physical quantities, like…
Riemann problems at geometric discontinuities are a classic and fascinating issue of hydraulics. In the present paper, the complete solution to the Riemann problem of the one-dimensional Shallow water Equations at monotonic width…