Related papers: Well-Balanced Hydrodynamics for the Piecewise Para…
The piecewise parabolic method and related schemes are widely used to model stellar flows. Several different methods for extending the validity of these methods to a general equation of state have been proposed over time, but direct…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and a reconstruction is termed `well-balanced' if it is able to simulate steady states at higher order than time…
We present a hydrodynamical code for cosmological simulations which uses the Piecewise Parabolic Method (PPM) to follow the dynamics of gas component and an N-body Particle-Mesh algorithm for the evolution of collisionless component. The…
Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed…
This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transforming the original non-linear system into a linearized kinetic…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium.…
We propose a methodology for designing well-balanced numerical schemes to investigate traveling waves in parabolic models from mathematical biology. We combine well-balanced techniques for parabolic models known in the literature with the…
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that…
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…
Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we…
In this paper I present a pedagogical derivation of continuity equations manifesting exact conservation laws in an interacting electronic system based on the nonequilibrium Keldysh technique. The purpose of this exercise is to lay the…
We show how hydrodynamics of relativistic system with broken continuous symmetry can be constructed using the Poisson bracket technique. We illustrate the method on the example of relativistic superfluids.