Related papers: Orbital Advection by Interpolation: A Fast and Acc…
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $\rho^e$. A time-discrete method based on the…
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection-diffusion problem within a more general Friedrichs system framework. With carefully constructed numerical traces, we introduce…
This work presents the publicly available moving-mesh magnetohydrodynamics code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach number. DISCO employs a moving-mesh…
Protoplanetary "transition" disks have large, mass-depleted central cavities, yet also deliver gas onto their host stars at rates comparable to disks without holes. The paradox of simultaneous transparency and accretion can be explained if…
The energy stable flux reconstruction (ESFR) method provides an efficient and flexible framework to devise high-order linearly stable numerical schemes which can achieve high levels of accuracy on unstructured grids. While superconvergent…
Grid-based magnetohydrodynamic (MHD) simulations have proven invaluable for the study of astrophysical accretion disks. However, the fact that angular momentum transport in disks is mediated by MHD turbulence (with structure down to very…
The stationary hydrodynamic equations for the transonic accretion disks and flows around rotating black holes are presented by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. We use two types…
Numerical simulations including magnetic fields have become important in many fields of astrophysics. Evolution of magnetic fields by the constrained transport algorithm preserves magnetic divergence to machine precision, and thus…
We investigated the instability of advective accretion flow as a consequence of angular momentum transfer in one-dimensional, quasi-spherical transonic accretion flow around a non-rotating black hole. The code is designed to include the…
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite…
Exascale supercomputing unleashes the potential for simulations of astrophysical systems with unprecedented resolution. Taking full advantage of this computing power requires the development of new algorithms and numerical methods that are…
This paper focuses on providing the high order algorithms for the space-time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being…
We present a new approach to Eulerian computational fluid dynamics that is designed to work at high Mach numbers encountered in astrophysical hydrodynamic simulations. The Eulerian fluid conservation equations are solved in an adaptive…
We develop a new numerical scheme for ideal magnetohydrodynamic (MHD) simulations, which is robust against one- and multi-dimensional shocks, and is accurate for low Mach number flows and discontinuities. The scheme belongs to a family of…
When gas accretes onto a black hole, at a rate either much less than or much greater than the Eddington rate, it is likely to do so in an "adiabatic" or radiatively inefficient manner. Under fluid (as opposed to MHD) conditions, the disk…
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to…
Context: Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. The radiation transport algorithm should be as fast…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system,…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…