Implementation of an efficient segregated algorithm-IDEAL on 3D collocated grid system

Sun, Defeng; Qu, Zhiguo; Tao, Wen‐Quan

doi:10.1007/s11434-009-0124-4

Cited by 16 publications

(7 citation statements)

References 35 publications

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“…And the exact solution of this case is the same as that of example, i.e. expression (15), and the corresponding Dirichlet BC can be easily derived by the exact solution. Here the tested points NT=1636 are uniformly distributed between the physical boundary and a square of boundary length 12.…”

Section: Example 3 Dirichlet Problem With An Epitrochoid Boundary Shamentioning

confidence: 95%

“…However, the MMFS demands a complex calculation of the diagonal elements of interpolation matrix. It is worthy of noting that, unlike the mesh methods [4][5][6][7][8]15,16], the MFS, RMM and MMFS do not require any meshes and are all meshless [17] in nature.Inspired by the pioneering work mentioned above, we propose a novel numerical method, called singular boundary …”

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confidence: 99%

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A novel numerical method for infinite domain potential problems

Chen

2010

Chin. Sci. Bull.

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The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community. This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems. The SBM is mathematically simple, easy-to-program, meshless and integration-free. To guarantee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation. The efficiency and accuracy of the proposed technique are tested to the three infinite domain potential problems.infinite domain, potential problem, singularity, fundamental solution, singular boundary method, meshless Citation:Chen W, Fu Z J. A novel numerical method for infinite domain potential problems.The infinite potential problems [1−3] have been observed in a wide variety of scientific and engineering fields, such as the ideal potential flow around a body, the electrostatic field and the steady temperature field, etc. However, the numerical solution to such problems still presents a great challenge so far to the communities of engineering simulation and scientific computing. Most of popular numerical methods such as finite element and finite volume methods need to truncate infinite domain to an artificial finite region with subtle artificial boundary conditions [4] or absorbing layers [5]. This truncation can be arbitrary largely based on trial-error experiences. On the other hand, the boundary element method (BEM) [6−8] appears very attractive to handle the unbounded domain problem because it applies the fundamental solution as the basis function, which satisfies the governing equation and the boundary condition at infinity. And no domain truncation is required. However, the singular or hyper-singular integrals [8] in the BEM are not mathematically simple and require additional computing costs.To avoid the singularities of fundamental solutions, the method of fundamental solutions (MFS) [9−11] distributes the boundary knots on fictitious boundary which is outside the physical domain, and the location of fictitious boundary is vital for the accuracy and reliability of the MFS solution. However, despite great efforts for decades, the determination of fictitious boundary is still arbitrary and tricky, largely based on experiences. Recently, Young et al. [12] proposed an alternative meshless method, namely regularized meshless method (RMM) [13] to remedy this drawback of the MFS. By employing the desingularization of subtracting and adding-back technique, the RMM can place the source points on the real physical boundary. In addition, the ill-conditioned interpolation matrix of BEM and MFS is also circumvented in the RMM. However, the original RMM requires the uniform distribution of nodes and severely reduces its applicability to complex-shaped boundary problems. Similar to the RMM, Sarler [14] proposed the modified method of fundamental solution (MMFS) to solve the potential flow problems. However, the MMFS demands a ...

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Section: Example 3 Dirichlet Problem With An Epitrochoid Boundary Shamentioning

confidence: 95%

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confidence: 99%

A novel numerical method for infinite domain potential problems

Chen

2010

Chin. Sci. Bull.

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“…14 It has been further extended and shown to work well for use on a variety of other problems including unsteady two phase flow, flow on highly skewed grids, and three dimensional collocated solvers. [15][16][17] However, IDEAL and SIMPLER are both iterative time advancement schemes and require relaxation of the momentum equations to ensure convergence. These aspects mean the algorithms can be computationally intensive for unsteady problems.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Pressure-Based Algorithm for Incompressible Flows

Garrick

Rajagopalan

2015

22nd AIAA Computational Fluid Dynamics Conference

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A new solution procedure called Diagonal Split Corrected Linked Equations via Operator splitting (DS-CLEO) has been developed for solving the momentum equations in the pressure-based SIMPLER-type formulation of the incompressible Navier-Stokes equations. An explicit momentum predictor step based on a time splitting procedure is shown to possess unconditional stability while only the implicit pressure equation requires a computationally intensive iterative solver. No relaxation of any of the governing equations is necessary to ensure convergence for either steady or unsteady problems. It is demonstrated that pressure-velocity coupling and second order time accuracy is obtained through a set of inner iterations on the pressure and velocity fields using the exact discretized equations. The Diagonal Split procedure offered a 33.9 and 35.9x reduction in runtime compared to SIMPLER for two unsteady problems tested and a minor runtime reduction for steady lid-driven cavity flow.

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“…Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of the solution process. The IDEAL algorithm has now been extended to the orthogonal coordinates [23][24][25] and the nonorthogonal curvilinear coordinates [26].…”

Section: Introductionmentioning

confidence: 99%

Performance Analyses of IDEAL Algorithm on Highly Skewed Grid System

Sun

Ding

2014

Advances in Mechanical Engineering

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IDEAL is an efficient segregated algorithm for the fluid flow and heat transfer problems. This algorithm has now been extended to the 3D nonorthogonal curvilinear coordinates. Highly skewed grids in the nonorthogonal curvilinear coordinates can decrease the convergence rate and deteriorate the calculating stability. In this study, the feasibility of the IDEAL algorithm on highly skewed grid system is analyzed by investigating the lid-driven flow in the inclined cavity. It can be concluded that the IDEAL algorithm is more robust and more efficient than the traditional SIMPLER algorithm, especially for the highly skewed and fine grid system. For example, at = 5 ∘ and grid number = 70 × 70 × 70, the convergence rate of the IDEAL algorithm is 6.3 times faster than that of the SIMPLER algorithm, and the IDEAL algorithm can converge almost at any time step multiple.

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Implementation of an efficient segregated algorithm-IDEAL on 3D collocated grid system

Cited by 16 publications

References 35 publications

A novel numerical method for infinite domain potential problems

A novel numerical method for infinite domain potential problems

An Explicit Pressure-Based Algorithm for Incompressible Flows

Performance Analyses of IDEAL Algorithm on Highly Skewed Grid System

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