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A dimension split method for the incompressible Navier–Stokes equations in three dimensions
International Journal for Numerical Methods in Fluids, 2013SUMMARYIn this paper, we describe a new method for the three‐dimensional steady incompressible Navier–Stokes equations, which is called the dimension split method (DSM). The basic idea of DSM is that the three‐dimensional space is split up into a cluster of two‐dimensional manifolds and then the three‐dimensional solution is approximated by the ...
Chen, H., Li, K., Wang, S.
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Engineering With Computers, 2021
By introducing the dimension splitting method into the reproducing kernel particle method (RKPM), a hybrid reproducing kernel particle method (HRKPM) for solving three-dimensional (3D) wave propagation problems is presented in this paper. Compared with the RKPM of 3D problems, the HRKPM needs only solving a set of two-dimensional (2D) problems in some ...
Yumin Cheng
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By introducing the dimension splitting method into the reproducing kernel particle method (RKPM), a hybrid reproducing kernel particle method (HRKPM) for solving three-dimensional (3D) wave propagation problems is presented in this paper. Compared with the RKPM of 3D problems, the HRKPM needs only solving a set of two-dimensional (2D) problems in some ...
Yumin Cheng
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The application of dimension split method in the three‐dimensional heat equation
Mathematical Methods in the Applied Sciences, 2016A dimension splitting method (DSM) with Crank–Nicolson time discrete strategy for a three‐dimensional heat equation is proposed. The basic idea is to simulate the three‐Dimensional problem by numerically solving a series of two‐dimensional problems in parallel fashion.
Zhao, Jianping +4 more
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A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions
Journal of Scientific Computing, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shi Jin 0003, Chunxiong Zheng
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Engineering Analysis With Boundary Elements, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhijuan Meng, Yumin Cheng
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhijuan Meng, Yumin Cheng
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A Dimension Splitting Method for 3-D Incompressible Thermal Flow
Numerical Heat Transfer, Part B: Fundamentals, 2015This 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.
Hao Chen +3 more
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An efficient dimension splitting p-adaptive method for the binary fluid surfactant phase field model
Computers & Mathematics with Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Na Xie +3 more
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Intermediate boundary corrections for split operator methods in three dimensions
BIT, 1967This paper deals with the intermediate boundary corrections required by splittings of alternating direction methods for solving three space dimensional problems involving Laplace's equation or the heat conduction equation. In addition to considering the existing splittings of Douglas and D'Yakonov, a new splitting is introduced.
Gourlay, A. R., Mitchell, A. R.
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The dimension splitting reproducing kernel particle method for three‐dimensional potential problems
International Journal for Numerical Methods in Engineering, 2019SummaryIn this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction.
P.P. Peng, Q. Wu, Y.M. Cheng
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A dimension split method for the 3‐D compressible Navier–Stokes equations in turbomachine
Communications in Numerical Methods in Engineering, 2001AbstractIn this paper, by using classical tensor calculus, we derive the compressible Navier–Stokes equation on a so‐called stream surface which is a two‐dimensional (2‐D) manifold that gives a definition of a stream function with the equation satisfied by it. Based on this, a new algorithm is proposed which is called dimension split algorithm.
Li, Kaitai +2 more
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