Nektar++: Enhancing the capability and application of high-fidelity spectral/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e862" altimg="si5.svg"><mml:mrow><mml:mi>h</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math> element methods

Moxey, David; Cantwell, Chris D.; Bao, Yan; Cassinelli, Andrea; Castiglioni, Giacomo; Chun, Seok-Ju; Juda, Emilia; Kazemi, Ehsan; Lackhove, Kilian; Marcon, Julian; Mengaldo, Gianmarco; Serson, Douglas; Turner, Michael G.; Xu, Hanlin; Peiró, Joaquim; Kirby, Robert M.; Sherwin, Spencer J.

doi:10.1016/j.cpc.2019.107110

Cited by 112 publications

(81 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we use the spectral/hp element methods formulation described in detail in reference [3] and implemented in Nektar++ [16,17]. We briefly describe the fundamentals of the methods in what follows.…”

Section: Continuous and Discontinuous Galerkin Spectral Element Methodsmentioning

confidence: 99%

“…To solve the Laplace problem (4) we use the open source spectral element program Nektar++ [16,17]. We first generate a triangular finite element mesh which is then made high order and curved by projecting interior nodes onto the curved boundaries [19].…”

Section: Solution Of the Field Equationsmentioning

confidence: 99%

“…We first generate a triangular finite element mesh which is then made high order and curved by projecting interior nodes onto the curved boundaries [19]. This procedure is carried out in NekMesh [17], which also has the capability to optimize the high order mesh should some elements be of low quality or simply invalid [20]. Such a mesh is shown in Fig.…”

Section: Solution Of the Field Equationsmentioning

confidence: 99%

See 2 more Smart Citations

A high resolution PDE approach to quadrilateral mesh generation

Marcon

Kopriva

Sherwin

et al. 2019

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of π/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.

show abstract

Section: Continuous and Discontinuous Galerkin Spectral Element Methodsmentioning

confidence: 99%

Section: Solution Of the Field Equationsmentioning

confidence: 99%

Section: Solution Of the Field Equationsmentioning

confidence: 99%

See 1 more Smart Citation

A high resolution PDE approach to quadrilateral mesh generation

Marcon

Kopriva

Sherwin

et al. 2019

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…We seek a discrete approximation within an element,

Ω^{e}

, of the form

u (x, t) \approx u_{h}^{e} (x, t) = \sum_{i = 1}^{N_{e l}} u_{i}^{e} (t) w_{i}^{e} (x); x \in Ω^{e},

where

w_{i}^{e} (x); i = 1, \dots, N_{e l}

represent the elemental expansion functions for the high‐order spectral/ hp DG method available in Nektar++ 16,17 . Both the solution and test functions are discontinuous at the interface between elements.…”

Section: Discontinuous Galerkin Discretizationmentioning

confidence: 99%

rp‐adaptation for compressible flows

Marcon

Castiglioni

Moxey

et al. 2020

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

We present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature‐based sensors or error estimators. We demonstrate this proof‐of‐concept using two geometries in transonic and supersonic flow regimes. The method has been implemented in the open‐source spectral/hp element framework Nektar++, and adaptivity is performed by its dedicated high‐order mesh generation tool NekMesh. The results show that the proposed rp‐adaptation methodology is a reasonably cost‐effective way of improving simulation accuracy.

show abstract

“…Continuous Galerkin (CG) [20], discontinuous Galerkin (DG) [24] and flux reconstruction (FR) schemes (currently only support hexahedral and quadrilateral meshes) [25] are supported for spatial discretizations. Up to 12 built-in solvers have been developed to date providing the capability of multi-solver coupling [26]. These solvers make the Nektar++ framework applicable to a wide range of simulations [6,26].…”

Section: Introductionmentioning

confidence: 99%

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Yan

Pan

Castiglioni

et al. 2021

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/hp element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/hp element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge-Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible tex, turbulent flow over a circular cylinder at Re = 3900 and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.

show abstract

Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods

Cited by 112 publications

References 65 publications

A high resolution PDE approach to quadrilateral mesh generation

A high resolution PDE approach to quadrilateral mesh generation

rp‐adaptation for compressible flows

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Contact Info

Product

Resources

About