Regularized singular boundary method for 3D potential flow

Kovářík, Karel; Mužík, Juraj; Masarovičová, Soňa; Sitányiová, Dana

doi:10.1016/j.enganabound.2018.06.022

Cited by 9 publications

(7 citation statements)

References 17 publications

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“…The OIFs associated with the Laplace fundamental solution can be determined using subtracting and adding-back technique for the normal derivative (Neumann) boundary condition [7], [13] where L j is the length of the appropriate part of boundary around point x i (see Fig. 1).…”

Section: Singular Boundary Methodsmentioning

confidence: 99%

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Multidomain Singular Boundary Method for 2d Laminar Viscous Flow

Mužík

Bulko

2018

WIT Transactions on Engineering Sciences

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In this paper, a numerical algorithm is developed for the solution of two-dimensional isothermal laminar viscous flow. The proposed numerical method implementation, which is quadrature-free, is based on the stream-velocity formulation of Navier-Stokes equations, the method of the particular solutions and the singular boundary method (SBM). The steady stream-velocity formulation of NS equation is 4th order biharmonic non-homogeneous nonlinear equation type which is solved using the proposed method with the non-homogeneous and nonlinear terms approximated using the method of particular solutions with multiquadrics RBF function. The accuracy of the method is proven using 2D backwardfacing step and lid-driven cavity test cases.

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Section: Singular Boundary Methodsmentioning

confidence: 99%

“…1). The value of the OIF for prescribed solution value (Dirichlet BC) on the boundary, the formula based on the regularized boundary integral equation is used [13]…”

Section: Singular Boundary Methodsmentioning

confidence: 99%

Multidomain Singular Boundary Method for 2d Laminar Viscous Flow

Mužík

Bulko

2018

WIT Transactions on Engineering Sciences

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“…This nonlinear system of differential equations has already been solved by a number of numerical methods, starting with the finite difference method through the finite element method to meshless and boundary type methods. The methods based on boundary integral theory are represented by the local boundary integral element method (LBIEM) [1], the boundary element method (BEM) [2], [3], the method of fundamental solutions (MFS) [4] and the singular boundary method (SBM) [5]. In the case of BEM the singularities of the fundamental solution are handled by proper integration method, the MFS overcomes the singularity using a fictitious boundary, but the optimum location of this boundary remains the open problem especially for complex-shaped domains.…”

Section: Introductionmentioning

confidence: 99%

“…To bypass the fictitious boundary construction, the SBM formulation adopts a concept of the origin intensity factors (OIFs). Several techniques have been developed to determine the source intensity factors, namely, inverse interpolation technique (IIT), subtracting and adding-back regularization and empirical formulas [5], [6].…”

Section: Introductionmentioning

confidence: 99%

The use of dual reciprocity method for 2D laminar viscous flow

Mužík

2020

MATEC Web Conf.

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The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

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“…Unfortunately, the BEM and the BCM encounter the singularity and hyper singularity difficulties [20][21][22] due to the application of the fundamental solutions. In recent years, many useful techniques are proposed to bypass this limitation, such as the logarithmic quadrature formulation [23], the rigid body motion method [24], the subtraction and adding-back technique (SAB) [25][26][27], the integration by parts [28], the analytical integration approach [29] and the contour method [30]. As a competitive strategy, the SAB technique was first proposed by Young et [31][32][33] in the regularized meshless method (RMM) [34][35][36].…”

Section: Introductionmentioning

confidence: 99%