Related papers: On the one-dimensional SPH approximation of fracti…
Obtaining a stable magnetohydrodynamical (MHD) formalism in SPH - i.e. smoothed particle magnetohydrodynamics (SPMHD) - has proven remarkably difficult. To implement MHD requires two steps: a modification to the momentum equation and an…
Simulations using the Smoothed Particle Hydrodynamics (SPH) technique typically include numerical viscosity to model shocks and maintain particle order on the kernel scale. This numerical viscosity is composed of linear and quadratic terms,…
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…
This work presents a new multiphase SPH model that includes the shifting algorithm and a variable smoothing length formalism to simulate multi-phase flows with accuracy and proper interphase management. The implementation was performed in…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
Many applications, such as system identification, classification of time series, direct and inverse problems in partial differential equations, and uncertainty quantification lead to the question of approximation of a non-linear operator…
We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves…
This study proposes a generalized coordinates based smoothed particle hydrodynamics (GSPH) method with overset methods using a Total Lagrangian (TL) formulation for large deformation and crack propagation problems. In the proposed GSPH, the…
In this study we investigated the capabilities of the mesh-free, Lagrangian particle method (Smoothed Particle Hydrodynamics, SPH) to simulate the detailed hydrodynamic processes generated by both spilling and plunging breaking waves within…
This review discusses Smoothed Particle Hydrodynamics (SPH) in the astrophysical context, with a focus on inviscid gas dynamics. The particle-based SPH technique allows an intuitive and simple formulation of hydrodynamics that has excellent…
In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which…
Modeling human operator's dynamic plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behaviour, a new kind of…
Accurate mesh-free simulation of fluid flows involving complex boundaries requires that the boundaries be captured accurately in terms of particles. In the context of incompressible/weakly-compressible fluid flow, the SPH method is more…
Various formulations of smooth-particle hydrodynamics (SPH) have been proposed, intended to resolve certain difficulties in the treatment of fluid mixing instabilities. Most have involved changes to the algorithm which either introduce…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
Computational fluid dynamics is a crucial tool to theoretically explore the cosmos. In the last decade, we have seen a substantial methodological diversification with a number of cross-fertilizations between originally different methods.…
This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth…
In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the…
Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…