Related papers: An implicit algorithm for simulating the dynamics …
A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
In this paper we introduce the concept of Direct Statistical Simulation (DSS) for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary…
Interstellar dust grains do not have a single well-defined origin. Stars are demonstrably dust producers, but also efficient destroyers of cosmic dust. Dust destruction in the ISM is believed to be the result of SN shocks hitting the…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
Simulating the flow of different fluids can be a highly computational intensive process, which requires large amounts of resources. Recently there has been a lot of research effort directed towards GPU processing, which can greatly increase…
We develop a computational method based on Dissipative Particle Dynamics (DPD) that introduces solvent hydrodynamic interactions to coarse-grained models of solutes, such as ions, molecules, or polymers. DPD-solvent (DPDS) is a fully…
We develop a numerical method for solving a free boundary problem which describes shape relaxation, by surface tension, of a long and thin bubble of an inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. The method of…
We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code {\small GADGET}. It is based on a fast, robust and photon-conserving integration scheme where the…
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 consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
We present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water…
Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain populations is mainly governed by fragmentation during pair-wise…
An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…
The present paper introduces stochastic velocity as improvement for moving particle semi-implicit (MPS) method. This improvement is to overcome energy loss caused by numerical dissipation in the basic MPS that brings about rapid decay of…
We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we combine, implement, modify and test a vast majority of SPH improvement…
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random…
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative…
We consider the acceleration of very small dust grains including Polycyclic Aromatic Hydrocarbons (PAHs) arising from the electrostatic interactions of dust grains that have charge fluctuations in time due to charging events. We simulate…