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A simple, efficient, and high-order accurate curved sliding-mesh interface approach to spectral difference method on coupled rotating and stationary domains

Bin Zhang, Chunlei Liang
2015 Journal of Computational Physics  
This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method.  ...  To verify the spatial order of accuracy of the sliding-mesh spectral difference (SSD) method, both inviscid and viscous flow cases are tested.  ...  The spectral difference (SD) method is one discontinuous high-order method for solving the conservation laws on unstructured grids [15, 32, 28, 11] .  ... 
doi:10.1016/j.jcp.2015.04.006 fatcat:xcba3aizung53b6t7nnxkec4kq

A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods [article]

Edward Laughton, Gavin Tabor, David Moxey
2021 arXiv   pre-print
how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality.  ...  With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand  ...  , in the construction of a spectral difference solver for the compressible Navier-Stokes equations that incorporates sliding grids by Zhang and Liang [27] and more recently in the hyperbolic solver FLEXI  ... 
arXiv:2007.15534v2 fatcat:a3u6eirmpjd25nfbimssdpcfcq

An Efficient Sliding Mesh Interface Method for High-Order Discontinuous Galerkin Schemes [article]

Jakob Dürrwächter, Marius Kurz, Patrick Kopper, Daniel Kempf, Claus-Dieter Munz, Andrea Beck
2020 arXiv   pre-print
The method is based on the mortar method and is high-order accurate. It can handle three-dimensional sliding mesh interfaces with various interface shapes.  ...  Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion.  ...  Manufactured Solution To verify the high-order accuracy of the implemented method for fully three-dimensional flows, a smooth manufactured solution from [47] is investigated.  ... 
arXiv:2008.04356v1 fatcat:lge4ou7uabggloeb4sdjuwj7hq

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

David Moxey, Chris D. Cantwell, Yan Bao, Andrea Cassinelli, Giacomo Castiglioni, Sehun Chun, Emilia Juda, Ehsan Kazemi, Kilian Lackhove, Julian Marcon, Gianmarco Mengaldo, Douglas Serson (+5 others)
2019 Computer Physics Communications  
solvers for partial differential equations using the high-order spectral/hp element method.  ...  Spectral/hp element methods High-order finite element methods a b s t r a c t Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of  ...  Semtex [15, 16] is a fluid dynamics code that also uses the classical spectral element method in two dimensions, with the use of a 1D pseudospectral Fourier expansion for three dimensional problems containing  ... 
doi:10.1016/j.cpc.2019.107110 fatcat:cfkq2f7z3jbtzayhsnn5uwcswe

A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments

Wei Leng, Lili Ju, Max Gunzburger, Stephen Price, Todd Ringler
2012 Journal of Geophysical Research  
A parallel finite element implementation on tetrahedral grids of the nonlinear three-dimensional nonlinear Stokes model for the dynamics of ice-sheets is presented.  ...  Discretization is based on a high-order accurate scheme using the Taylor-Hood element pair. Both no-slip and sliding boundary conditions at the ice-bedrock boundary are studied.  ...  Among the numerous different types of approaches employed, the three-dimensional nonlinear Stokes ice-sheet model appears to be a widely accepted method owing to its capability for dealing with realistic  ... 
doi:10.1029/2011jf001962 fatcat:dsiwbrgq3jbvhitr2khkmqrfla

Nektar++: enhancing the capability and application of high-fidelity spectral/hp element methods [article]

David Moxey, Chris D. Cantwell, Yan Bao, Andrea Cassinelli, Giacomo Castiglioni, Sehun Chun, Emilia Juda, Ehsan Kazemi, Kilian Lackhove, Julian Marcon, Gianmarco Mengaldo, Douglas Serson (+5 others)
2019 arXiv   pre-print
Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp  ...  Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic  ...  Semtex [15, 16] is a fluid dynamics code that also uses the classical spectral element method in two dimensions, with the use of a 1D pseudospectral Fourier expansion for three dimensional problems that  ... 
arXiv:1906.03489v2 fatcat:nlz3erpuzjenvbjetfbdv4nxc4

Solution of Nonlinear Stokes Equations Discretized By High-Order Finite Elements on Nonconforming and Anisotropic Meshes, with Application to Ice Sheet Dynamics

Tobin Isaac, Georg Stadler, Omar Ghattas
2015 SIAM Journal on Scientific Computing  
Motivated by the need for efficient and accurate simulation of the dynamics of the polar ice sheets, we design high-order finite element discretizations and scalable solvers for the solution of nonlinear  ...  In a numerical study, we find that our solver yields fast convergence that is independent of the element aspect ratio, the occurrence of nonconforming interfaces, and of mesh refinement, and that depends  ...  Several issues related to high-order, adaptive mesh discretizations and solvers for the simulation of nonlinear Stokes flow in three-dimensional anisotropic domains are addressed in this work.  ... 
doi:10.1137/140974407 fatcat:kkbmilkxvvh5tivtgwrfujebzm

High-order gas-kinetic scheme in general curvilinear coordinate for iLES of compressible wall-bounded turbulent flows [article]

Guiyu Cao, Kun Xu, Liang Pan, Minping Wan, Shiyi Chen
2021 arXiv   pre-print
The iLES results with HGKS-cur are in good agreement with the refereed spectral methods and high-order finite volume methods.  ...  The two-stage fourth-order method, which was developed for spatial-temporal coupled flow solvers, is used for temporal discretization.  ...  The authors would like to thank TaiYi supercomputers in the SUSTech for providing high performance computational resources.  ... 
arXiv:2107.08609v1 fatcat:ulgwnzsibnentfojjfemqeahsq

Sliding Basis Optimization for Heterogeneous Material Design [article]

Nurcan Gecer Ulu, Svyatoslav Korneev, Erva Ulu, Saigopal Nelaturi
2020 arXiv   pre-print
The sliding basis framework is independent of any particular physics analysis, objective and constraints, providing a versatile and powerful design optimization tool for various applications.  ...  We further improve computational efficiency by using the property that the Laplacian eigenfunctions form a spectrum and may be ordered from lower to higher frequencies.  ...  [43] presents a reduced order method for surface design.  ... 
arXiv:2005.08838v1 fatcat:emgnf6tnpbgelgrxfv47otmbqq

A Parallel Implementation of a Spectral Element Ocean Model for Simulating Low-Latitude Circulation System [chapter]

H. Ma, J. McCaffrey, S. Piacsek
1998 Parallel Computational Fluid Dynamics 1997  
The present work shows that the high-order domain decomposition methods can be efficiently implemented in a massively parallel computing env u-onment to solve large-scale CFD problems, such as the general  ...  This paper is about the parallel implementation of a high-resolution, spectral element, primitive equation model of~ahomogeneous equatorial ocean.  ...  The main difference between the spectral element method and the spectral multi-domain method is that the Co and Cl boundary conditions at the interface of the elements have to be enforced explicitly in  ... 
doi:10.1016/b978-044482849-1/50077-4 dblp:conf/pcfd/MaMP97 fatcat:kdg33clx7ffpfdso4fomnfxgvy

Special issue on finite-size particles, drops and bubbles in fluid flows: advances in modelling and simulations

Cristian Marchioli, Stéphane Vincent
2019 Acta Mechanica  
libraries within the solver (iterative, spectral).  ...  A more fundamental study has been performed by Andersson and Jiang [1] , who use the IBM to study the motion of the three-dimensional flow field around a prolate spheroid with fixed aspect ratio, fixed  ... 
doi:10.1007/s00707-018-2352-7 fatcat:abru2tw4fna43m5biixcy6oagi

An implicit hybrid method for the computation of rotorcraft flows

M. A. Woodgate, G. N. Barakos
2018 Aeronautical Journal  
A common interface should also be required to allow for ease of use. However, it is very time consuming to develop, maintain and add extra functionally to different codes.  ...  The paper presents some of the challenges encountered in extending the code which was written for a single mesh type, to a more flexible solver that is still computationally efficient but can cope with  ...  The authors would like to acknowledge the use of the NICETRIP model geometry, the EPSRC/eCSE programme for the use of the ARCHER high performance computer and the West of Scotland Computing service ARCHIE-WeSt  ... 
doi:10.1017/aer.2018.108 fatcat:bz4c7kvc3ncgxf44ceudup2fcy

A two stage fourth-order gas-kinetic scheme on unstructured hybrid mesh [article]

Dongxin Pan and Chengwen Zhong and Congshan Zhuo
2017 arXiv   pre-print
For generalized Riemann problem and Navier-Stokes solution, the gas-kinetic scheme (GKS) provides a time-accurate flux solver using a different way in the reconstruction at a cell interface in which two  ...  To achieve fourth order accuracy, a finite volume method for GKS using cubic spline reconstruction is proposed on both structured grid and unstructured hybrid mesh.  ...  NUMERICAL RESULTS Couette flow For planar Couette flow, the fluid flows between a surface sliding with a constant velocity, U ∞ , and a stationary surface, is simulated under different mesh sizes to  ... 
arXiv:1711.07850v1 fatcat:uc5aztfk6zfczf4hzsjep37bfm

An overset mesh approach for 3D mixed element high-order discretizations

Michael J. Brazell, Jayanarayanan Sitaraman, Dimitri J. Mavriplis
2016 Journal of Computational Physics  
The goal of this work is to devise an accurate, efficient and robust three-15 dimensional high-order method based on DG discretizations [23] for simu-16 lating a wide variety of compressible flows in an  ...  and its implementation for three-dimensional 61 problems.  ...  Liang, A Simple, Efficient, High-Order Accurate Sliding-545 mesh Interface Approach to FR/CPR Method on Coupled Rotating and 546 Stationary Domains, American Institute of Aeronautics and Astronau-547 tics  ... 
doi:10.1016/j.jcp.2016.06.031 fatcat:rzwfvd4eezhzje72cipv4jbdfa

rp ‐adaptation for compressible flows

Julian Marcon, Giacomo Castiglioni, David Moxey, Spencer J. Sherwin, Joaquim Peiró
2020 International Journal for Numerical Methods in Engineering  
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.  ...  We present a novel rp-adaptation strategy for high-fidelity simulations of compressible inviscid flows with shocks.  ...  The use of high-order spectral/hp element methods in the simulation of compressible fluid dynamics is now becoming increasingly common for high-fidelity large-eddy simulations and direct numerical simulations  ... 
doi:10.1002/nme.6529 fatcat:kgwfn2f4fvffrod2d57fkqox3m
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