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Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
This review is a short introduction to numerical hydrodynamics in a cosmological context, intended for the non specialist. The main processes relevant to galaxy formation are first presented. The fluid equations are then introduced, and…
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We present results obtained from a set of cosmological hydrodynamic simulations of galaxy clusters, aimed at comparing predictions with observational data on the diversity between cool-core (CC) and non-cool-core (NCC) clusters. Our…
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes…
We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of…
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…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
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…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…
The primary objective of this thesis is to develop a consistent theoretical framework of dissipative hydrodynamics for a relativistic fluid with spin - hereafter referred to as relativistic dissipative spin hydrodynamics. In this framework,…
Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic…
We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are…
Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they…
We present version 1.0 of our Lagrangian Numerical Relativity code SPHINCS_BSSN. This code evolves the full set of Einstein equations, but contrary to other Numerical Relativity codes, it evolves the matter fluid via Lagrangian particles in…
We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a…