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Improvement to Patched Grid Technique with High-Order Conservative Remapping Method

Yufei Zhang, Haixin Chen, Song Fu
2011 Journal of Aircraft  
As an example, for the Jameson cell-centered finite volume method with a piecewise-constant reconstruction on the mismatched surface, the flux on the cell surface (j, k + 4) can be written as : FLUX og  ...  The flux is then computed with the Riemann solver and, finally, the flux is summed up for a grid cell to get its total flux on the interface. b) Embedded block for the mending plate | | | L c) Surface  ... 
doi:10.2514/1.c031093 fatcat:xxe5xeeckredvcp7zogztsgiqe

A technique of flux reconstruction at the interfaces of non‐conforming grids for aeroacoustic simulations

S. Le Bras, H. Deniau, C. Bogey
2019 International Journal for Numerical Methods in Fluids  
In a first section, the high-order finite-volume approach 73 used in this study and the flux reconstruction method for conforming interfaces are described. 74 In section 2, the reconstruction technique  ...  SUMMARY A flux reconstruction technique is presented in order to perform aeroacoustic computations using implicit high-order spatial schemes on multiblock structured grids with non-conforming interfaces  ...  +1/2 U i+3/ Figure 2 . 2 et al. [12] demonstrated that the numerical scheme (11) is equivalent to Lele's 6th-order finite-123 difference scheme [11] for a uniform Cartesian mesh.  ... 
doi:10.1002/fld.4767 fatcat:mk6wgfbpybgpjj4yjqzxvnefh4

Compact upwind schemes on adaptive octrees

Scott M. Murman
2010 Journal of Computational Physics  
Compact high-order upwind schemes using reconstruction from cell-averages are derived for application with the compressible three-dimensional Navier-Stokes equations.  ...  Numerical examples for smooth flows demonstrate the improvement over explicit upwind schemes and formal accuracy of the schemes, as well as the behavior in wall-bounded regions, and the resolution of a  ...  Karim Shariff of NASA Ames Research Center for suggesting the spectral forcing method to generate isotropic turbulence.  ... 
doi:10.1016/j.jcp.2009.10.019 fatcat:6wwzxofaandsllbab4kdl25bfe

High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows

Lucian Ivan, Clinton P.T. Groth
2014 Journal of Computational Physics  
A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of the Navier-Stokes equations  ...  The high-order viscous (elliptic) fluxes are computed based on a k-order accurate gradient derived from the same unlimited high-order reconstructions.  ...  De Sterck of the Applied Mathematics Department at the University of Waterloo for offering support to this research.  ... 
doi:10.1016/j.jcp.2013.09.045 fatcat:y2kt56dntvhwrjda6agwwvxehy

2D Validation Of A High-Order Adaptive Cartesian-Grid Finite-Volume Characteristic- Flux Model With Embedded Boundaries

C. Leroy, G. Oger, D. Le Touzé, B. Alessandrini
2011 Zenodo  
A Finite Volume method based on Characteristic Fluxes for compressible fluids is developed.  ...  An explicit cell-centered resolution is adopted, where second and third order accuracy is provided by using two different MUSCL schemes with Minmod, Sweby or Superbee limiters for the hyperbolic part.  ...  Finite Volume Characteristic Flux (FVCF) schemes The FCVF scheme, proposed by Ghidaglia et al [1] in 1996, is a finite volume scheme with cell centered variables, including the kinetic vector.  ... 
doi:10.5281/zenodo.1054823 fatcat:vu5lyag235a4zl52juy2r4isay

Flux-conserving treatment of non-conformal interfaces for finite-volume discretization of conservation laws

Enrico Rinaldi, Piero Colonna, Rene Pecnik
2015 Computers & Fluids  
We present a new flux-conserving treatment of non-conformal mesh block interfaces for the numerical solution of conservation laws by high order finite volumes schemes.  ...  presents a new flux-conserving treatment of non-conformal interfaces for the nu-46 merical solution of conservation laws by high order finite volumes schemes.  ...  First order 361 accuracy was used for the convective flux discretization and the Euler equations were integrated 362 in time with the explicit RK3 method and the implicit backward Euler scheme.  ... 
doi:10.1016/j.compfluid.2015.07.017 fatcat:j66tvcs5wvffxjiyra3jyy4aby

An Implicit Block LU-SGS Algorithm-Based Lattice Boltzmann Flux Solver for Simulation of Hypersonic Flows

Z. X. Meng
2019 Advances in Applied Mathematics and Mechanics  
In this method, the finite volume method (FVM) is applied to discretize the Navier-Stokes equations, and the LBFS is utilized to evaluate the numerical flux at the cell interface.  ...  In order to improve the robustness and convergence rate of the simulation for hypersonic flows, especially for problems with complex geometry, the implicit block LU-SGS algorithm is introduced to solve  ...  Different from the conventional CFD approaches, which only compute the flux by numerical approximation, the Boltzmann equation-based schemes evaluate the flux through a local reconstruction with the solution  ... 
doi:10.4208/aamm.oa-2018-0167 fatcat:an5yqoaxgfdz5mjtz4fotzkaoe

A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

Ricardo Costa, Gaspar J. Machado, Stéphane Clain
2015 International Journal of Applied Mathematics and Computer Science  
A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed.  ...  First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving  ...  To design a numerical scheme, we replace the exact fluxes F i± 1 2 with numerical fluxes up to a sixth-order accuracy F i± 1 2 (Φ) depending on the vector Φ.  ... 
doi:10.1515/amcs-2015-0039 fatcat:3s3lznvy25hprinr4iil5qjm6q

Rocket Combustion Chamber Simulations Using High-Order Methods [chapter]

Timo Seitz, Ansgar Lechtenberg, Peter Gerlinger
2020 Notes on Numerical Fluid Mechanics and Multidisciplinary Design  
This numerical scheme is utilized to investigate three different rocket combustors, namely a seven injector methane/oxygen combustion chamber, the widely simulated PennState preburner combustor and a single  ...  High-order spatial discretizations significantly improve the accuracy of flow simulations.  ...  The simulation of the last test case was also funded by the DLR project Tauros. Computational resources have been provided by the High Performance Computing Center Stuttgart (HLRS).  ... 
doi:10.1007/978-3-030-53847-7_24 fatcat:jjb2a2vbd5h4dmblrh5kildybq

Research on Computational Method of Supersonic Inlet/Isolator Internal Flow

Zhuoran Liu, Caizheng Wang, Ke Zhang, Zhuo Zhao, Zhifeng Xie
2021 Applied Sciences  
In this research, a CFD solver is developed for solving the 2D/3D compressible flowproblem: the finite volume method based on multi-block structural grids is used to solve thecompressible Reynolds averaged  ...  Included in the methodology aremultiple high-order reconstruction schemes, such as the 3rd-order MUSCL (Monotone UpstreamcenteredSchemes for Conservation Laws), 5th-order WENO (Weight Essentially Non-Oscillatory  ...  Acknowledgments: Thanks are due to Yufei Zhang, Jingyuan Wang and Dongdong Zhong of Tsinghua University for valuable discussion. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/app11199272 fatcat:omnmzxwaefenzn5arboayfhh3i

A Comparative Study of 2D Numerical Methods with GPU Computing [article]

Ben J. Zimmerman, Jonathan D. Regele, Bong Wie
2017 arXiv   pre-print
It is shown that while FV methods can produce solutions with low computational times, they produce larger errors than high-order methods for smooth problems at the same order of accuracy.  ...  However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of problems.  ...  Approved for unlimited release: LA-UR-17-27957.  ... 
arXiv:1709.01619v1 fatcat:4hhxtxsxijglrhoyhji7qp2wxm

A lattice Boltzmann approach for free-surface-flow simulations on non-uniform block-structured grids

Christian Janssen, Manfred Krafczyk
2010 Computers and Mathematics with Applications  
The additional advection equation for the volume-of-fluid (VOF) fill level is discretized with a classical finite volume method.  ...  For the interface reconstruction, a piecewise linear interface reconstruction in 3D has been implemented.  ...  In this work, we develop and employ a flux-based advection scheme and compare both split and unsplit schemes for two different surface reconstruction methods.  ... 
doi:10.1016/j.camwa.2009.08.064 fatcat:kbsstkgiprbxdij5ch7z3xl2xy

A parallel compact-TVD method for compressible fluid dynamics employing shared and distributed-memory paradigms

Vincenzo Fico, David R. Emerson, Jason M. Reese
2011 Computers & Fluids  
method for compressible fluid dynamics employing shared and distributed-memory paradigms' Abstract A novel multi-block compact-TVD finite difference method for the simulation of compressible flows is  ...  In our approach a domain decomposition technique is applied to a compact scheme using explicit flux formulas at block interfaces.  ...  continuity of the numerical flux function across block-interfaces.  ... 
doi:10.1016/j.compfluid.2010.12.025 fatcat:lspjyjyp35fplifoqa4ohmt6lm

High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

L. Ivan, H. De Sterck, A. Susanto, C.P.T. Groth
2015 Journal of Computational Physics  
A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on threedimensional (3D) cubed-sphere grids is described.  ...  Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions.  ...  Section 2 describes our fourth-order accurate finite-volume scheme for conservation laws on 3D cubed-sphere grids, using a high-order polynomial reconstruction approach with CENO monotonicity enforcement  ... 
doi:10.1016/j.jcp.2014.11.002 fatcat:5kesvwrilncypb7gl7wf4rmd5e

Improvement of the computational performance of a parallel unstructured WENO finite volume CFD code for Implicit Large Eddy Simulation

Panagiotis Tsoutsanis, Antonis F. Antoniadis, Karl W. Jenkins
2018 Computers & Fluids  
The code is assessed on five different HPC systems; significant speed-up is achieved ranging from 1.5 to 8.5, with very high-order schemes benefiting the most.  ...  The present higher-order WENO methods are producing significantly smaller errors for a series of test problems, compared to a standard 2nd-order Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme  ...  Acknowledgements The authors would like to acknowledge the computing time at HAZELHEN at the High-Performance Computing Center Stuttgart (HLRS), Germany and SuperMUC at the Leibniz Supercomputing Centre  ... 
doi:10.1016/j.compfluid.2018.03.012 fatcat:xqspcavfa5d4diqes5hiq3auyq
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