Related papers: A Fast Numerical Scheme for Causal Relativistic Hy…
We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…
We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the…
For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…
Continuing on our previous work [ArXiv:1212.2644], we develop semi-implicit numerical methods for solving low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with…
We present a class of relativistic fluid models for cold and dense matter with bulk viscosity, whose equilibrium equation of state is polytropic. These models reduce to Israel-Stewart theory for small values of the viscous stress $\Pi$.…
Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of…
In this paper, we present a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obeys the thermodynamical laws. The obtained numerical schemes are…
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 propose several linear, fully decoupled numerical schemes with first- and second-order temporal accuracy for a novel Q-tensor-based two-phase hydrodynamic model describing the coupling of active nematic liquid crystal solutions with…
We study periodic solutions to the Navier-Stokes equations. The transition phase of a dynamic Navier-Stokes solution to the periodic-in-time state can be excessively long and it depends on parameters like the domain size and the viscosity.…
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…
We present an alternative approach to deriving second-order non-conformal hydrodynamics from the relativistic Boltzmann equation. We demonstrate how constitutive relations for shear and bulk stresses can be transformed into dynamical…
The Swift--Hohenberg equation is a widely studied fourth-order model, originally proposed to describe hydrodynamic fluctuations. It admits an energy-dissipation law and, under suitable assumptions, bounded solutions. Many…
We present the first numerical solutions of the causal, stable relativistic Navier-Stokes equations as formulated by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). For this initial investigation we restrict to plane-symmetric configurations…
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes…
When one considers a shock wave in the frame where the shock is at rest, on either side one has a steady flow which converges to equilibrium away from the shock. However, hydrodynamics is unable to describe this flow if the asymptotic…
The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…