17 research outputs found
Hydrodynamic simulations with the Godunov SPH
We present results based on an implementation of the Godunov Smoothed
Particle Hydrodynamics (GSPH), originally developed by Inutsuka (2002), in the
GADGET-3 hydrodynamic code. We first review the derivation of the GSPH
discretization of the equations of moment and energy conservation, starting
from the convolution of these equations with the interpolating kernel. The two
most important aspects of the numerical implementation of these equations are
(a) the appearance of fluid velocity and pressure obtained from the solution of
the Riemann problem between each pair of particles, and (b the absence of an
artificial viscosity term. We carry out three different controlled
hydrodynamical three-dimensional tests, namely the Sod shock tube, the
development of Kelvin-Helmholtz instabilities in a shear flow test, and the
"blob" test describing the evolution of a cold cloud moving against a hot wind.
The results of our tests confirm and extend in a number of aspects those
recently obtained by Cha (2010): (i) GSPH provides a much improved description
of contact discontinuities, with respect to SPH, thus avoiding the appearance
of spurious pressure forces; (ii) GSPH is able to follow the development of
gas-dynamical instabilities, such as the Kevin--Helmholtz and the
Rayleigh-Taylor ones; (iii) as a result, GSPH describes the development of curl
structures in the shear-flow test and the dissolution of the cold cloud in the
"blob" test.
We also discuss in detail the effect on the performances of GSPH of changing
different aspects of its implementation. The results of our tests demonstrate
that GSPH is in fact a highly promising hydrodynamic scheme, also to be coupled
to an N-body solver, for astrophysical and cosmological applications.
[abridged]Comment: 19 pages, 13 figures, MNRAS accepted, high resolution version can be
obtained at
http://adlibitum.oats.inaf.it/borgani/html/papers/gsph_hydrosim.pd
Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics
In this paper, we develop a new method for magnetohydrodynamics (MHD) using
smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the
Godunov method is applied to SPH instead of artificial dissipation terms. In
the interaction between particles, we solve a nonlinear Riemann problem with
magnetic pressure for compressive waves and apply the method of characteristics
for Alfv{\'e}n waves. An extensive series of MHD test calculations is
performed. In all test calculations, we compare the results of our SPH code
with those of a finite-volume method with an approximate Riemann solver, and
confirm excellent agreement.Comment: 22 pages, 20 figures, accepted for Monthly Notices of Royal
Astronomical Societ
Astrophysical Weighted Particle Magnetohydrodynamics
This paper presents applications of weighted meshless scheme for conservation
laws to the Euler equations and the equations of ideal magnetohydrodynamics.
The divergence constraint of the latter is maintained to the truncation error
by a new meshless divergence cleaning procedure. The physics of the interaction
between the particles is described by an one-dimensional Riemann problem in a
moving frame. As a result, necessary diffusion which is required to treat
dissipative processes is added automatically. As a result, our scheme has no
free parameters that controls the physics of inter-particle interaction, with
the exception of the number of the interacting neighbours which control the
resolution and accuracy. The resulting equations have the form similar to SPH
equations, and therefore existing SPH codes can be used to implement the
weighed particle scheme. The scheme is validated in several hydrodynamic and
MHD test cases. In particular, we demonstrate for the first time the ability of
a meshless MHD scheme to model magneto-rotational instability in accretion
disks.Comment: 27 pages, 24 figures, 1 column, submitted to MNRAS, hi-res version
can be obtained at http://www.strw.leidenuniv.nl/~egaburov/wpmhd.pd
A Stable Hybrid Potential–SPH Technique to Enforce the Fluid Incompressibility
The SPH method has extensively used in fluid flow simulation. Through SPH the fluid is modelled by
a particles system whose mutual interaction is weighed by a function, named kernel function, whose limits define
the neighbouring of each particle. In spite of the high capabilities of SPH for simulate complex environments, it
shows shortcomings specially if the fluid is subject to high changes in the pressure, the velocity and the density
as occur in phenomena such as shock–tube, blast–wave or in the boundary and discontinuities where the number
of neighbour particles is relatively low. In this case, the pressure gradient is inaccurate. As consequence, the
simulation is instable with an erratic behaviour of particles. To avoid this problem, we propose a hybrid technique.
This one consists in formulating the pressure gradient from a potential defined on each particles pair. Thus, the
pressure gradient is immune to the low number of neighbour particles. Also, our proposal allows enforcing the
fluid incompressibility. To show the improvements obtained we will carry out a set of simulationMinisterio de Economía y Competitividad TIN2016-76953-C3-2-
Blended numerical schemes for the advection equation and conservation laws
In this paper we propose a method to couple two or more explicit numerical
schemes approximating the same time-dependent PDE, aiming at creating new
schemes which inherit advantages of the original ones. We consider both
advection equations and nonlinear conservation laws. By coupling a macroscopic
(Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of
multiscale numerical method
GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
We present two new Lagrangian methods for hydrodynamics, in a systematic
comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The
new methods are designed to simultaneously capture advantages of both
smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement
(AMR) schemes. They are based on a kernel discretization of the volume coupled
to a high-order matrix gradient estimator and a Riemann solver acting over the
volume 'overlap.' We implement and test a parallel, second-order version of the
method with self-gravity & cosmological integration, in the code GIZMO: this
maintains exact mass, energy and momentum conservation; exhibits superior
angular momentum conservation compared to all other methods we study; does not
require 'artificial diffusion' terms; and allows the fluid elements to move
with the flow so resolution is automatically adaptive. We consider a large
suite of test problems, and find that on all problems the new methods appear
competitive with moving-mesh schemes, with some advantages (particularly in
angular momentum conservation), at the cost of enhanced noise. The new methods
have many advantages vs. SPH: proper convergence, good capturing of
fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical
viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing.
Advantages vs. non-moving meshes include: automatic adaptivity, dramatically
reduced advection errors & numerical overmixing, velocity-independent errors,
accurate coupling to gravity, good angular momentum conservation and
elimination of 'grid alignment' effects. We can, for example, follow hundreds
of orbits of gaseous disks, while AMR and SPH methods break down in a few
orbits. However, fixed meshes minimize 'grid noise.' These differences are
important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code,
user's guide, test problem setups, and movies are available at
http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm
Recommended from our members
Improved MLPG_R method for simulating 2D interaction between violent waves and elastic structures
Interaction between violent water waves and structures is of a major concern and one of the important issues that has not been well understood in marine engineering. This paper will present first attempt to extend the Meshless Local Petrov Galerkin method with Rankine source solution (MLPG_R) for studying such interaction, which solves the Navier-stokes equations for water waves and the elastic vibration mequations for structures under wave impact. The MLPG_R method has been applied successfully to modeling various violent water waves and their interaction with rigid structures in our previous publications. To make the method robust for modeling wave elastic-structure interaction
(hydroelasticity) problems concerned here, a near-strongly coupled and partitioned procedure is proposed to deal with coupling between violent waves and dynamics of structures. In addition, a novel approach is adopted to estimate pressure gradient when updating velocities and positions of fluid particles, leading to a relatively smoother pressure time history that is crucial for success in simulating problems about wavestructure interaction. The developed method is used to model several cases, covering a range from small wave to violent waves. Numerical results for them are compared with those obtained from other methods and from experiments in literature. Reasonable good agreement between them is achieved
Blended numerical schemes for the advection equation and conservation laws
In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating a new scheme which inherits advantages of the original ones. We consider both advection equations and nonlinear conservation laws. By coupling a macroscopic (Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of multiscale numerical method
From Mesh to Meshless : a Generalized Meshless Formulation Based on Riemann Solvers for Computational Fluid Dynamics
Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01[Abstract]
From mesh to meshless: A generalized meshless formulation based on Riemann
solvers for Computational Fluid Dynamics
This thesis deals with the development of high accuracy meshless methods for the simulation
of compressible and incompressible flows. Meshless methods were conceived to
overcome the constraints that mesh topology impose on traditional mesh-based numerical
methods. Despite the fact that meshless methods have achieved a relative success
in some particular applications, the truth is that mesh-based methods are still the
preferred choice to compute flows that demand high-accuracy. Instead of assuming
that meshless and mesh-based methods are groups of methods that follow independent
development paths, in this thesis it is proposed to increase the accuracy of meshless
methods by taking guidance of some successful techniques adopted in the mesh-based
community.
The starting point for the development is inspired by the SPH-ALE scheme proposed
by Vila. Especially, the flexibility of the ALE framework and the introduction
of Riemann solvers are essential elements adopted. High accuracy is obtained by using
the Moving Least Squares (MLS) technique. MLS serves multiple tasks in the implemented
scheme: high order reconstruction of Riemann states, more accurate viscous
flux evaluation and the replacement of the limited kernel approximation by MLS approximation
with polynomial degree consistency by design. The stabilization of the
scheme for compressible flows with discontinuities is based on a posteriori stabilization
technique (MOOD) that introduces a great improvement compared with the traditional
a priori flux limiters.
The MLSPH-ALE scheme is the first proposed meshless formulation that uses high
order consistent MLS approximation in a versatile ALE framework. In addition, the
procedure to obtain the semi-discrete formulation keeps track of a boundary term,
which eases the implementation of the boundary conditions.
Another important contribution is related with the general concept of the MLSPHALE
formulation. The MLSPH-ALE scheme is proved to be a global meshless formulation
that under some particular settings provides the same semi-discrete equations
that other meshless formulations published.
The MLSPH-ALE scheme has been tested for the computation of turbulent flows.
The low dissipation inherent to the Riemann solver is compatible with the implicit LES turbulent model. The proposed formulation is able to capture the energy cascade in
the subsonic regime where traditional SPH formulations are reported to fail.[Resumen]
Desde métodos con malla a métodos sin malla: Una formulación sin malla
generalizada basada en solvers de Riemann para Dinámica de Fluidos
Computacional
Esta tesis aborda el desarrollo de métodos sin malla de alta precisión para la simulación
de flujos compresibles e incompresibles. Los métodos sin malla fueron creados
para superar las restricciones que la conectividad de la malla impone a los métodos
tradicionales. A pesar de haber alcanzado un ´éxito relativo en algunas aplicaciones, la
realidad es que los métodos con malla siguen siendo la opción preferida para el cálculo
de flujos que demandan alta precisión. En vez de asumir que métodos sin malla y con
malla son grupos de métodos que siguen caminos de desarrollo independientes, en esta
tesis se propone incrementar la precisión de los métodos sin malla tomando como guía
algunas de las técnicas más exitosas empleadas en la comunidad de los métodos con
malla.
El punto de partida para el desarrollo se inspira en el esquema SPH-ALE propuesto
por Vila. De manera especial, la flexibilidad del marco de referencia ALE y la introducción
de los solvers de Riemann son elementos esenciales adoptados. La alta precisión
se obtiene con la técnica de Mínimos Cuadrados Móviles (MLS). MLS sirve múltiples
funciones en la implementación del esquema: alto orden de reconstrucción de los estados
de Riemann, evaluaciones más precisas de los flujos viscosos y reemplazo de la
aproximación limitada tipo kernel por una aproximación MLS con un grado de consistencia
polinómica arbitraria. La estabilización del esquema para flujos compresibles
con discontinuidades se basa en una técnica de estabilización a posteriori (MOOD) que
introduce una importante mejora con respecto a los tradicionales limitadores de flujo
a priori.
El esquema MLSPH-ALE es la primera formulación sin malla propuesta que utiliza
la aproximación MLS de alto orden en un marco de referencia ALE. Además, el procedimiento
dado para obtener la forma semi-discreta realiza el seguimiento de un término
en la frontera del dominio que facilita la implementación discreta de las condiciones de
contorno.
Otra importante contribución está relacionada con el concepto general de la formulación MLSPH-ALE. Se ha demostrado que el esquema MLSPH-ALE es una formulación sin malla global que con ciertas configuraciones particulares es capaz de proporcionar
las mismas formas semi-discretas que otras formulaciones publicadas.
El método MLSPH-ALE ha sido puesto a prueba frente al cálculo de flujos turbulentos.
La baja disipación inherente a los solver de Riemann hace que el esquema sea
apto para modelar la turbulencia en un contexto de modelos implícitos LES. La formulación propuesta es capaz de capturar la cascada de energía en el rango de régimen
subsónico donde los métodos tradicionales presentan fallos.[Resumo]
Desde métodos con malla a métodos sen malla: Unha formulación sen malla
xeneralizada baseada en solvers de Riemann para Dinámica de Fluidos
Computacional.
Esta tese trata sobre o desenvolvemento de métodos sen malla de alta precisión para a
simulación de fluxos compresibles e incompresibles. Os métodos sen malla foron creados
para superar as restricións que a conectividade da malla impón sobre os métodos
tradicionais. A pesar de ter acadado un éxito relativo nalgunhas aplicacións, a realidade
é que os métodos con malla seguen sendo a opción preferente para o cálculo de
fluxos que demandan alta precisión. No canto de asumir que os métodos sen malla
e con malla son grupos que seguen camiños de desenvolvemento independentes, nesta
tese proponse incrementar a precisión dos métodos sen malla tomando como guía
algunha das técnicas de máis éxito empregadas na comunidade dos métodos con malla.
O punto de partida para o desenvolvemento inspírase no esquema SPH-ALE proposto
por Vila. A flexibilidade do marco de referencia ALE e a introducción dos solvers
de Riemann son os elementos esenciais utilizados nesta tese. A alta precisión acádase
coa técnica de Mínimos Cadrados Móbiles (MLS). MLS serve para múltiples tarefas
na implementación do esquema: acadar alto orde de reconstrución nos estados de Riemann,
avaliacións máis precisas dos fluxos viscosos e troco da aproximación limitada
tipo kernel por unha aproximación MLS con grado de consistencia polinómica arbitraria.
A estabilización do esquema para fluxos compresibles con descontinuidades baséase
nunha técnica de estabilización a posteriori (MOOD) que introduce unha importante
mellora con respecto a os tradicionais limitadores de fluxo a priori.
O esquema MLSPH-ALE ´e a primeira formulación sen malla proposta que emprega
a técnica de aproximación MLS con alta consistencia nun marco de referencia ALE.
Ademais, o procedemento seguido para obter a forma semi-discreta realiza o seguimento
dun termo na fronteira que facilita a implementación das condicións de contorno.
Outra importante contribución relacionase co concepto xeral da formulación MLSPHALE
proposta. Demostrase que o esquema MLSPH-ALE é unha formulación sen malla
global que con certas configuración particulares rende as mesmas formas semi-discretas
que outras formulacións publicadas.
O método MLSPH-ALE foi posto a proba fronte o cálculo de fluxos turbulentos. A
baixa disipación implícita aportada polo solver de Riemann fai que o esquema sexa apto
para acometer o modelado da turbulencia cos modelos implícitos LES. A formulación
proposta captura a cascada de enerxía no rango de réxime subsónico, onde os métodos
tradicionais SPH presentan deficiencias.This work has been partially supported by the Ministerio de Ciencia, Innovación
y Universidades (RTI2018-093366-B-100) of the Spanish Government and by the Consellería de Educación e Ordenación Universitaria of the Xunta de Galicia, cofinanced
with FEDER funds and the Universidade da Coruña