Related papers: An approach to the Riemann problem for SPH invisci…
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…
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…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave…
For the past 20 years, our approach to shock capturing in smoothed particle hydrodynamics (SPH) has been to use artificial viscosity and conductivity terms supplemented by switches to control excess dissipation away from shocks (Monaghan…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
This paper proposes a novel numerical method based on Godunov Smoothed Particle Hydrodynamics for special relativistic fluid dynamics. Our method utilizes a Riemann solver to describe shock, enhancing accuracy in strong shock waves. The…
In smooth-particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial…
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 paper proposes a way to control the viscosity of numerical approximation in the contact SPH method. This variant of SPH contains momentum and energy fluxes in the right-hand sides of the equations, which are calculated using the…
This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that…
The ghost fluid method allows a propagating interface to remain sharp during a numerical simulation. The solution of the Riemann problem at the interface provides proper information to determine interfacial fluxes as well as the velocity of…
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…
We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing…
We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…
Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…