A Finite-Volume Particle Method for Compressible Flows

Hietel, Dietmar; Steiner, Klaus; Struckmeier, Jens

doi:10.1142/s0218202500000604

Cited by 78 publications

(58 citation statements)

References 11 publications

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“…Hietel et al 2000). Various authors have pointed out how matrix and least-squares methods can be used to define consistent, higher-order gradient operators, and renormalization schemes can be used to eliminate the zeroth-order errors of methods like SPH (see e.g.…”

Section: A New Numerical Methodology For Hydrodynamicsmentioning

confidence: 99%

A new class of accurate, mesh-free hydrodynamic simulation methods

Hopkins¹

2015

Monthly Notices of the Royal Astronomical Society

1,072

1,023

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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: 1 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.

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Section: A New Numerical Methodology For Hydrodynamicsmentioning

confidence: 99%

A new class of accurate, mesh-free hydrodynamic simulation methods

Hopkins¹

2015

Monthly Notices of the Royal Astronomical Society

1,072

1,023

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“…In this section, we explain the main ingredients of the finite volume particle method (FVPM) [10], which we use as a prototype for an Eulerian particle-based concept in numerical flow simulation. In previous work [13], we have also introduced a semiLagrangian particle method (SLPM).…”

Section: Finite Volume Particle Methods (Fvpm)mentioning

confidence: 99%

“…The combination between Voronoi diagrams and finite volumes yields through the basic concept of the FVPM a flexible particle method for the numerical solution of (1), (2). We further remark that a more general concept of the FVPM [10,14], allows for overlapping influence areas {V Ξ (ξ )} ξ ∈Ξ in which case, however, the FVPM needs to be combined with a partition of unity method (PUM). This provides more flexibility, but it leads to a more complicated FVPM discretization.…”

Section: Finite Volume Particle Methods (Fvpm)mentioning

confidence: 99%

On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

Iske

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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This contribution discusses the construction of kernel-based adaptive particle methods for numerical flow simulation, where the finite volume particle method (FVPM) is used as a prototype. In the FVPM, scattered data approximation algorithms are required in the recovery step of the WENO reconstruction. We first show how kernel-based approximation schemes can be used in the recovery step of particle methods, where we give preference to the radial polyharmonic spline kernel. Then we discuss important aspects concerning the numerical stability and approximation behaviour of polyharmonic splines. Moreover, we propose customized coarsening and refinement rules for the adaptive resampling of the particles. Supporting numerical examples and comparisons with other radial kernels are provided.

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“…FVPM is a particle-based solver introduced by Hietel et al (2000) in 2000, Nestor et al (2009 extended the method to incompressible flows. This method features an Arbitrary Lagrangian-Eulerian (ALE) formulation, which means that the computing nodes can either move with the material velocity or a user-prescribed velocity.…”

Section: Numerical Simulationmentioning

confidence: 99%

Toward design optimization of a Pelton turbine runner

Vessaz

Andolfatto

Avellan

et al. 2016

Struct Multidisc Optim

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The objective of the present paper is to propose a strategy to optimize the performance of a Pelton runner based on a parametric model of the bucket geometry, massive particle based numerical simulations and advanced optimization strategies to reduce the dimension of the design problem. The parametric model of the Pelton bucket is based on four bicubic Bézier patches and the number of free parameters is reduced to 21. The numerical simulations are performed using the finite volume particle method, which benefits from a conservative, consistent, arbitrary Lagrangian Eulerian formulation. The resulting design problem is of High-dimension with Expensive Black-box (HEB) performance function. In order to tackle the HEB problem, a preliminary exploration is performed using 2'000 sampled runners geometry provided by a Halton sequence.

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A Finite-Volume Particle Method for Compressible Flows

Cited by 78 publications

References 11 publications

A new class of accurate, mesh-free hydrodynamic simulation methods

A new class of accurate, mesh-free hydrodynamic simulation methods

On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

Toward design optimization of a Pelton turbine runner

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