Related papers: Hyperbolic Divergence Cleaning for SPH
Silent data corruptions (SDCs) hinder the correctness of long-running scientific applications on large scale computing systems. Selective particle replication (SPR) is proposed herein as the first particle-based replication method for…
It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of…
We present a 'two-fluid' implementation of dust in smoothed particle hydrodynamics (SPH) in the test particle limit. The scheme is able to handle both short and long stopping times and reproduces the short friction time limit, which is not…
Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In the standard SPH method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this…
The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
Basic Smoothed Particle Hydrodynamics (SPH) models exhibit excessive, numerical dissipation in the simulation of water wave propagation. This can be remedied using higher-order approaches such as kernel gradient correction, which introduce…
Magnetic fields play an important role in astrophysics on a wide variety of scales, ranging from the Sun and compact objects to galaxies and galaxy clusters. Here we discuss a novel implementation of ideal magnetohydrodynamics (MHD) in the…
The present work proposes an approach for fluid-solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes-Cahn-Hilliard (NSCH) model in the Eulerian framework, while few investigations have been made in the Lagrangian…
We adapt the spectral viscosity (SV) formulation implemented as a modal filter to a Spectral Difference Method (SD) solving hyperbolic conservation laws. In the SD Method we use selections of different orthogonal polynomials (APK…
This work presents a theoretical formalism and the corresponding numerical techniques to obtain the approximation of fractional-order operators over a 1D domain via the smoothed particle hydrodynamics (SPH) method. The method is presented…
Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…
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…