A high-order spectral difference method for unstructured dynamic grids

Yu, Meilin; Wang, Zhi Jian; Hu, Haoran

doi:10.1016/j.compfluid.2011.03.015

Cited by 49 publications

(57 citation statements)

References 28 publications

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“…The performance of the developed solver for low Mach number flow is first tested by computing the steady viscous flow over a NACA0012 airfoil at Re¼ 5000, Ma ∞ ¼ 0.05 and zero AOA with a 3rd order accurate SD scheme and an implicit LU-SGS time integration (Yu et al, 2011) on a coarse mesh. The residual convergence history, pressure coefficient (C P ) contour, and the Mach number contour are displayed in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…2. Grid deformation strategy associated with the kinematics of the airfoil can be found in the paper by Yu et al (2011). The aerodynamic parameters are specified as follows.…”

Section: Simulation Parametersmentioning

confidence: 99%

“…Numerical simulations are carried out with an unsteady compressible Navier-Stokes solver using dynamic unstructured grid based high-order SD method developed in Yu et al (2011) and Sun et al (2006). The 2D unsteady compressible NavierStokes equation in conservation form reads,…”

Section: Governing Equationsmentioning

confidence: 99%

“…Some recent work on the numerical simulations of bio-inspired flow with high-order methods (e.g. Visbal, 2009;Visbal et al, 2009;Persson et al, 2010;Liang et al, 2010;Yu et al, 2011;Ou et al, 2011) has provided impressive results for the community and demonstrated the potential of the high-order numerical simulation in unsteady flapping-wing aerodynamics. The simulations in the present paper are carried out using the high-order accurate dynamic grid Navier-Stokes flow solver.…”

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confidence: 97%

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High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

Wang

2013

Journal of Fluids and Structures

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Section: Resultsmentioning

confidence: 99%

“…2. Grid deformation strategy associated with the kinematics of the airfoil can be found in the paper by Yu et al (2011). The aerodynamic parameters are specified as follows.…”

Section: Simulation Parametersmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

mentioning

confidence: 97%

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High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

Wang

2013

Journal of Fluids and Structures

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“…Mohammad et al [32] carried out LES of flow past a cylinder, Parsani et al [34] studied flow induced noise, Lodato et al [28] did wall modeled LES, Ou et al [33] and Yu et al [49] applied the SD method to moving grids, to name just a few. As pointed out by Bassi and Rebay [1,2], for high-order methods involving curved boundaries, the use of high-order elements is crucial for achieving smooth solution and for improving robustness, examples for the SD method can be found in [22,24].…”

Section: The Sd Methodsmentioning

confidence: 99%

A 2 D parallel high-order sliding and deforming spectral difference method

et al. 2016

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An implicit high‐order preconditioned flux reconstruction method for low‐Mach‐number flow simulation with dynamic meshes

Wang

2019

Numerical Methods in Fluids

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Summary A fully implicit high‐order preconditioned flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier‐Stokes equations at low Mach numbers. A dual‐time stepping approach with the second‐order backward differentiation formula (BDF2) is employed to ensure temporal accuracy for unsteady flow simulation. When dynamic meshes are used to handle moving/deforming domains, the geometric conservation law is implicitly enforced to eliminate errors due to the resolution discrepancy between BDF2 and the spatial FR/CPR discretization. The large linear system resulted from the spatial and temporal discretizations is tackled with the restarted generalized minimal residual solver in the PETSc (portable, extensible toolkit for scientific computation) library. Through several benchmark steady and unsteady numerical tests, the preconditioned FR/CPR methods have demonstrated good convergence and accuracy for simulating flows at low Mach numbers. The new flow solver is then used to study the effects of Mach number on unsteady force generation over a plunging airfoil when operating in low‐Mach‐number flows. It is observed that weak compressibility has a significant impact on thrust generation but has a negligible effect on lift generation of an oscillating airfoil.

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A high-order spectral difference method for unstructured dynamic grids

Cited by 49 publications

References 28 publications

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

A 2 D parallel high-order sliding and deforming spectral difference method

An implicit high‐order preconditioned flux reconstruction method for low‐Mach‐number flow simulation with dynamic meshes

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