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University of Kansas
1.
Jia, Feilin.
Towards industrial large eddy simulation using the FR/CPR method.
Degree: PhD, Aerospace Engineering, 2019, University of Kansas
URL: http://hdl.handle.net/1808/29660 
► NASA’s 2030 CFD Vision calls for the development of accurate and efficient scale-resolving simulations for turbulent flow, such as large eddy simulation (LES) and direct…
(more)
▼ NASA’s 2030 CFD Vision calls for the development of accurate and efficient scale-resolving simulations for turbulent flow, such as large eddy simulation (LES) and direct numerical simulation (DNS). This is primarily because the Reynolds-averaged Navier-Stokes (RANS) approach has failed to predict vortex-dominated flow involving large flow separations, e.g., flow through a jet engine or over aircraft near the edge of the flight envelope, i.e., during take-off and landing at high angles of attack. Although the DNS approach resolves all turbulence scales, it is too expensive in the foreseeable future for real world flow problems because of the disparate length and time scales in the flow. LES resolves the energetic large scales while modeling the smaller scales, so it provides a good compromise between accuracy and cost. As a result, LES is widely considered to be the method of choice for next generation CFD design tool. The major obstacle for LES is its considerable computational cost since unsteady 3D simulations need to be performed to obtain the mean flow quantities such as the drag and lift coefficients. In order to resolve the dominant scales in a turbulent flow, numerical methods used for LES should have low dissipation and dispersion errors. This means standard second order finite-volume methods are usually not accurate or efficient enough for LES applications. High-order methods (order of accuracy 2) have demonstrated their potential for LES and DNS in the past decade because of their low embedded numerical dissipation and dispersion errors. In the present study, we develop and demonstrate a recently developed high-order method, called flux reconstruction (FR) or correction procedure via reconstruction (CPR), for industrial LES. A major advantage of the FR/CPR method is its capability to handle unstructured mixed meshes, and its compactness and scalability, which is particularly desired on modern super-computers. We therefore address the following major pacing items in industrial LES in the present study: High-order methods Geometric flexibility Efficient time integration Efficient implementation on modern super computers Demonstration for real world applications
Advisors/Committee Members: Taghavi, Ray (advisor), J.%22%29&pagesize-30">
Wang,
Z.
J. (advisor),
Taghavi, Ray (cmtemember),
J.%22%29&pagesize-30">Wang, Z.J. (cmtemember),
Farokhi, Saeed (cmtemember),
Zheng, Zhongquan (cmtemember),
Shontz, Suzanne M (cmtemember).
Subjects/Keywords: Aerospace engineering; computational fluid dynamics; correction procedure via reconstruction; flux reconstruction; high order method; implicit time scheme
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APA (6th Edition):
Jia, F. (2019). Towards industrial large eddy simulation using the FR/CPR method. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/29660
Chicago Manual of Style (16th Edition):
Jia, Feilin. “Towards industrial large eddy simulation using the FR/CPR method.” 2019. Doctoral Dissertation, University of Kansas. Accessed March 03, 2021.
http://hdl.handle.net/1808/29660.
MLA Handbook (7th Edition):
Jia, Feilin. “Towards industrial large eddy simulation using the FR/CPR method.” 2019. Web. 03 Mar 2021.
Vancouver:
Jia F. Towards industrial large eddy simulation using the FR/CPR method. [Internet] [Doctoral dissertation]. University of Kansas; 2019. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/1808/29660.
Council of Science Editors:
Jia F. Towards industrial large eddy simulation using the FR/CPR method. [Doctoral Dissertation]. University of Kansas; 2019. Available from: http://hdl.handle.net/1808/29660
University of Kansas
2.
Shi, Lei.
Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.
Degree: PhD, Aerospace Engineering, 2014, University of Kansas
URL: http://hdl.handle.net/1808/27533
► High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems…
(more)
▼ High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems in the 1st International Workshop on High-Order Methods. For non-smooth problems, solution based hp-adaptations offer the best promise. Adjoint-based adaptive methods have the capability of dynamically distributing computing resources to areas which are important for predicting engineering performance parameters, such as lift or drag. This thesis presents a robust and efficient adjoint-based adaptive high-order differential formulation for the compressible Navier-Stokes equations, which can rapidly determine an accurate estimate of an engineering output within a prescribed error threshold. The flux reconstruction (FR) or the correction procedure via reconstruction (CPR) method used in this work is a high-order differential formulation. We develop a parallel adjoint-based adaptive CPR solver which can work with any element-based error estimate and handle arbitrary discretization orders for mixed elements. First, a dual-consistent discrete form of the CPR method is derived. Then, an efficient and accurate adjoint-based error estimation method for the CPR method is developed and its accuracy and effectiveness are verified for the linear and non-linear partial differential equations (PDE). For anisotropic h-adaptations, we use a local output error sampling procedure to find the optimal refinement option. The current method has been applied to aerodynamic problems. Numerical tests show that significant savings in the number of DOFs can be achieved through the adjoint-based adaptation.
Advisors/Committee Members: J.%22%29&pagesize-30">
Wang,
Z.
J. (advisor),
Farokhi, Saeed (cmtemember),
Huang, Weizhang (cmtemember),
Taghavi, Ray (cmtemember),
Tu, Xuemin (cmtemember),
Zheng, Zhongquan (cmtemember).
Subjects/Keywords: Aerospace engineering; Adaptive Method; Adjoint-based Adaptation; Computational Fluid Dynamics; High-order Method; Navier-Stokes Equations
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Shi, L. (2014). Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27533
Chicago Manual of Style (16th Edition):
Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Doctoral Dissertation, University of Kansas. Accessed March 03, 2021.
http://hdl.handle.net/1808/27533.
MLA Handbook (7th Edition):
Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Web. 03 Mar 2021.
Vancouver:
Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2014. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/1808/27533.
Council of Science Editors:
Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Doctoral Dissertation]. University of Kansas; 2014. Available from: http://hdl.handle.net/1808/27533
3.
Wang, Bin.
Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.
Degree: PhD, Mathematics, 2017, University of Kansas
URL: http://hdl.handle.net/1808/27005
► Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite…
(more)
▼ Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite elements in terms of accuracy and efficiency. The impact of this method is partly evidenced by the prolificacy of research work in this area. Weak Galerkin (WG) is a relatively newly proposed method by introducing weak functions and generalizing the differential operator for them. This method has also drawn remarkable interests from both numerical practitioners and analysts recently. HDG and WG are different but closely related. BDDC algorithms are developed for numerical solution of elliptic problems with both methods. We prove that the optimal condition number estimate for BDDC operators with standard finite element methods can be extended to the counterparts arising from the HDG and WG methods, which are nonconforming finite element methods. Numerical experiments are conducted to verify the theoretical analysis. Further, we propose BDDC algorithms for the saddle point system arising from the Stokes equations using both HDG and WG methods. By design of the preconditioner, the iterations are restricted to a benign subspace, which makes the BDDC operator effectively positive definite thus solvable by the conjugate gradient method. We prove that the algorithm is scalable in the number of subdomains with convergence rate only dependent on subdomain problem size. The condition number bound for the BDDC preconditioned Stokes system is the same as the optimal bound for the elliptic case. Numerical results confirm the theoretical analysis.
Advisors/Committee Members: Tu, Xuemin (advisor), Huang, Weizhang (cmtemember), Van Vleck, Erik (cmtemember), Xu, Hongguo (cmtemember), J.%22%29&pagesize-30">
Wang,
Z.
J. (cmtemember).
Subjects/Keywords: Mathematics; BDDC; domain decomposition; hybridizable discontinuous Galerkin; saddle point problems; Stokes; weak Galerkin
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wang, B. (2017). Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27005
Chicago Manual of Style (16th Edition):
Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Doctoral Dissertation, University of Kansas. Accessed March 03, 2021.
http://hdl.handle.net/1808/27005.
MLA Handbook (7th Edition):
Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Web. 03 Mar 2021.
Vancouver:
Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/1808/27005.
Council of Science Editors:
Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/27005
4.
Zhou, Cheng.
Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations.
Degree: PhD, Aerospace Engineering, 2016, University of Kansas
URL: http://hdl.handle.net/1808/24139
► The use of high-order methods to compute turbulent flows governed by the Reynolds- averaged Navier-Stokes (RANS) equations is an active research topic in the compu-…
(more)
▼ The use of high-order methods to compute turbulent flows governed by the Reynolds- averaged Navier-Stokes (RANS) equations is an active research topic in the compu- tational fluid dynamics (CFD) community. However, it is well known that high-order methods for the non-smooth turbulence modeling equations are difficult to converge to the steady-state because of the numerical stiffness. The objective of this work is to de- velop a robust and efficient high-order discretization that can simulate turbulent flows governed by the Reynolds-Averaged Navier-Stokes equations, which involves the de- velopment of high-order space discretization of robust turbulence modeling equations, the improvement of time integration strategy, and the application of effective mesh adaptation methods. In the present study, correction procedure via reconstruction (CPR) high-order dis- cretization is developed to solve the Reynolds-averaged Navier-Stokes (RANS) equa- tions with the modified Spalart and Allmaras (SA) model. In this model, the non- dimensional length scale depends on the distance to the nearest wall. To compute the distance of each solution point in the domain to the nearest curved polynomial wall boundaries, the CPR high-order discretization is extended to solve the Eikonal equa- tion. On the other hand, to improve time integration strategy for the simulation of turbulent flows, the present work carried out a comparative study of several implicit time integration schemes to determine which is the most efficient, robust and general scheme. Additionally, an adjoint-based adaptive mesh refinement method is utilized to minimize the output error. Numerical results show that, to achieve a certain level of accuracy, the adaptive CPR discretization of the RANS equations with the SA model saves orders of magnitude in terms of number of degrees of freedom comparing to the numerical results of uniform mesh refinement, when applied to the simulations of turbulent flows.
Advisors/Committee Members: J.%22%29&pagesize-30">
Wang,
Z.
J. (advisor),
Farokhi, Saeed (cmtemember),
Taghavi, Ray (cmtemember),
Tu, Xuemin (cmtemember),
Zheng, Zhongquan Charlie (cmtemember).
Subjects/Keywords: Aerospace engineering; Mathematics; Adaptive; CFD; CPR; High-order method; RANS
Record Details
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Record Details
Similar Records
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zhou, C. (2016). Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/24139
Chicago Manual of Style (16th Edition):
Zhou, Cheng. “Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations.” 2016. Doctoral Dissertation, University of Kansas. Accessed March 03, 2021.
http://hdl.handle.net/1808/24139.
MLA Handbook (7th Edition):
Zhou, Cheng. “Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations.” 2016. Web. 03 Mar 2021.
Vancouver:
Zhou C. Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2021 Mar 03].
Available from: http://hdl.handle.net/1808/24139.
Council of Science Editors:
Zhou C. Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/24139
. 
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