Streamline integration as a method for two-dimensional elliptic grid generation

Wiesenberger, Matthias; Held, Markus; Einkemmer, Lukas

doi:10.1016/j.jcp.2017.03.056

Cited by 8 publications

(21 citation statements)

References 28 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3 Topology and Geometry Here, we introduce data structures and functions that represent the concepts of Topology and Geometry and operations defined on them (for example the discontinuous Galerkin discretization of derivatives [21]). The geometries extension implements a large variety of grids and grid generation algorithms that can be used here [60,61].…”

Section: Overviewmentioning

confidence: 99%

“…Our efforts to enable three-dimensional simulations include the flux-coordinate independent approach within the discontinuous Galerkin framework [33], which we are the first to apply to full-F gyro-fluid models [57,30]. Recent studies focus on numerical elliptic grid generation [60,61]. Both are important for the efficient description of realistic magnetic field geometries.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Wiesenberger

Einkemmer

Held

et al. 2019

Computer Physics Communications

Self Cite

View full text Add to dashboard Cite

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two-and three-dimensional drift-and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique.We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. We briefly discuss alternative methods to ensure the correctness of results like the convergence of reduced physical quantities of interest, ensemble simulations, invariants or reduced simulation times.In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 10 −1 and 10 3 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak).

show abstract

Section: Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Wiesenberger

Einkemmer

Held

et al. 2019

Computer Physics Communications

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the solution of problems of interest in computational fluid dynamics, orthogonality or near-orthogonality next to boundaries are usually desirable, since according to [11], the accuracy on the discretization and boundary condition imposition is greatly improved. In case of a boundary corresponding to a wall, orthogonality and reduced grid spacing next to the wall are necessary in order to diminish the errors in the calculation of the large gradient of properties present in the boundary layer.…”

Section: Contour Orthogonalitymentioning

confidence: 99%

“…Finally, it is important to emphasize that, although some might consider grid generation a solved issue, this is not really true for some specialized applications [10]. An example is the case of multiply-connected domains with heterogeneous media; this is accentuated by fact that recent works have been addressing the subject, such as [10] and [11]. This is the primary reason for the interest in the present work.…”

Section: Introductionmentioning

confidence: 96%

On a Grid Generation Method Based Upon Inhomogeneous Elliptic Partial Differential Equations

Conde¹,

Garcia²,

Azevedo³

2019

Proceedings of the 5th World Congress on Mechanical, Chemical, and Material Engineering

View full text Add to dashboard Cite

A nearly-orthogonal boundary-conforming grid generation technique based upon inhomogeneous elliptic partial differential equations is presented. The method has been designed to generate grids for multiply-connected domains in a block-structure fashion. It also allows for control of point distribution along boundaries, as well as control of grid spacing inside the domain by using a slightly modified version of the renowned Thompson's control functions, which is reported to work well. Although not fully-automatic, the process is automatized in order to make it more usable and speed-up computational time, which is usually a demotivating factor in elliptic grid generation techniques. This is also the reason why the implementation has been performed in an objected-oriented fashion using C++ and as relaxation method the Alternating Direction Implicit (ADI) with-sequence, generating appealing results. The method presented can be fully extended to 3D. Some results are presented and discussed.

show abstract

“…However, these issues do not directly manifest in the grid points themselves. In fact, with the help of streamline integration [14,15] it is fairly straightforward to numerically construct grid points that are aligned with the flux-surfaces. What is unclear is whether • these then actually represent a (homeomorphic) coordinate transformation,…”

Section: Introductionmentioning

confidence: 99%

Streamline integration as a method for structured grid generation in X-point geometry

Wiesenberger

Held

Einkemmer

et al. 2018

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

We investigate structured grids aligned to the contours of a two-dimensional flux-function with an X-point (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the flux-function vanishes at the X-point. In general, this condition is sufficient for the existence of a structured aligned grid with an X-point. With the help of streamline integration we then propose a numerical grid construction algorithm. In a suitably chosen monitor metric the Laplacian of the flux-function vanishes at the X-point such that a grid construction is possible.We study the convergence of the solution to elliptic equations on the proposed grid. The diverging volume element and cell sizes at the X-point reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the X-point in practical applications. We show that grid refinement in the cells neighbouring the X-point restores the expected convergence rate.

show abstract

Streamline integration as a method for two-dimensional elliptic grid generation

Cited by 8 publications

References 28 publications

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

On a Grid Generation Method Based Upon Inhomogeneous Elliptic Partial Differential Equations

Streamline integration as a method for structured grid generation in X-point geometry

Contact Info

Product

Resources

About