A dimension split method for the 3‐D compressible Navier–Stokes equations in turbomachine

Li, Kaitai; Huang, Aixiang; Zhang, Wen ling

doi:10.1002/cnm.459

Cited by 40 publications

(19 citation statements)

References 5 publications

(5 reference statements)

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“…However, the algorithm is still complex, because generation of two classes of stream surface is a trouble some thing, therefore significant emphasis in the literature has been placed on developing simplified formulations of the stream surface approach. Especially, Kaitai Li and co-workers recently introduced a dimension splitting method (DSM) [11][12][13] for three-dimensional flow. The method is very promising and can be regarded as a renovation of Wu's S1=S2 approach because, as in Wu's S1=S2 theory, three-dimensional flow computation can be translated into a series of two-dimensional computations in the DSM, which does not need to generate a three-dimensional mesh.…”

Section: A Dimension Splitting Methods For 3-d Incompressible Thermal mentioning

confidence: 99%

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

Chen

Yang

et al. 2015

Numerical Heat Transfer, Part B: Fundamentals

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This work deals with the computation of three-dimensional incompressible thermal flow, and a dimension splitting method is proposed for this. First, a time-space iterative method is adopted to obtains Euler implicit=explicit scheme. For the remaining Stokes equations we present a projection method to deal with the incompressibility constraint. In conclusion, only three independent linear elliptic equations need to be calculated at each step. Furthermore, on account of the splitting property of the method, all the computations are carried out on two-dimensional manifolds, which greatly reduces the difficulty and the computational cost in mesh generation, and a coarse-grained parallel algorithm can be constructed.

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Section: A Dimension Splitting Methods For 3-d Incompressible Thermal mentioning

confidence: 99%

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

Chen

Yang

et al. 2015

Numerical Heat Transfer, Part B: Fundamentals

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“…According to rule of tensor transformation [17,18], the covariant and contravariant components of metric tensor of 3D Euclidian space 3 in new curvilinear coordinate system are, respectively, given by…”

Section: Curvilinear Coordinate Systemmentioning

confidence: 99%

Optimal shape design for blade's surface of an impeller via the Navier–Stokes equations

Gao

2005

Commun. Numer. Meth. Engng.

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SUMMARYIn this paper, a new principle of geometric design for blade's surface of an impeller is established. This is a thorough mathematical investigation of a shape control problem for the optimal design of an impeller's blade while 3D rotating Navier-Stokes equations are as the state equations in the control problem. The objective is to design the blade such that the viscous drag is minimized. Establishing a new curvilinear coordinate system, we depart from a standard domain transformation commonly used in the engineering literature and utilizing it we rephrase the design problem in one on a ÿxed domain. Certain advantages of our approach as no need for mesh regeneration and node redistribution and 3D mesh quality improvement are evident. Furthermore, in new coordinate system, it is easy to obtain gradient of optimal functional with respect to the surface of blade and to derive Euler-Lagrange equations for optimal solution which is an elliptic boundary value problem of fourth order. Moreover, we give the conjugate gradient algorithm for the control problem.

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“…Instead of decomposing the spatial domain, it splits the 3D problem into a series of two-dimensional (2D) problems. Recently, Li and his coworkers [10][11][12][13] extended the dimensional splitting method to the compressible Navier-Stokes equations and the linear elastic shell based on differential geometry and tensor analysis. Hou and Wei [7] presented a finite element DSA for the 3D elliptic equation in cartesian coordinates.…”

Section: Introductionmentioning

confidence: 99%

Adaptive dimension splitting algorithm for three-dimensional elliptic equations

Wei

Hou

Song

2014

International Journal of Computer Mathematics

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An adaptive dimension splitting algorithm for three-dimensional (3D) elliptic equations is presented in this paper. We propose residual and recovery-based error estimators with respect to X − Y plane direction and Z direction, respectively, and construct the corresponding adaptive algorithm. Two-sided bounds of the estimators guarantee the efficiency and reliability of such error estimators. Numerical examples verify their efficiency both in estimating the error and in refining the mesh adaptively. This algorithm can be compared with or even better than the 3D adaptive finite element method with tetrahedral elements in some cases. What is more, our new algorithm involves only two-dimensional mesh and one-dimensional mesh in the process of refining mesh adaptively, and it can be implemented in parallel.

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A dimension split method for the 3‐D compressible Navier–Stokes equations in turbomachine

Cited by 40 publications

References 5 publications

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

Optimal shape design for blade's surface of an impeller via the Navier–Stokes equations

Adaptive dimension splitting algorithm for three-dimensional elliptic equations

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