Local singular boundary method for two-dimensional steady and unsteady potential flow

Kovářík, Karel; Mužík, Juraj; Bulko, Roman; Sitányiová, Dana

doi:10.1016/j.enganabound.2019.08.013

Cited by 9 publications

(3 citation statements)

References 26 publications

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“…The localization of the global SBM is realized by adopting the finite collocation approach [8]. The set of points covers the computational domain Ω with global boundary Γ, and the neighbouring nodes create the local domain around each node (Fig.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The main drawback of this approach is the increase in the number of equations caused by the necessary compatibility equations at the boundary of the subdomain. The promising principle of finite collocation (FC), as formulated by Stevens et al [7], showed the potential to formulate indirect methods locally without a need to create and manage subdomains [8]. Like other local methods, the method defines a set of simple overlapping subdomains around the points at which the solution of the corresponding partial differential equation (PDE) is evaluated.…”

Section: Introductionmentioning

confidence: 99%

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Localized Singular Boundary Method for Solving the Convection–diffusion Equation With Variable Velocity Field

Mužík

Bulko

2022

WIT Transactions on Engineering Sciences

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This paper focuses on deriving the local variant of the singular boundary method (SBM) to solve the convection-diffusion equation. Adopting the combination of an SBM and finite collocation, one obtains the localized variant of SBM. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows solving velocity vector variable tasks, which is a problem with global SBM. The article presents the steady numerical example for the convection-diffusion problem with variable velocity field and examines the dependence of the accuracy of the solution on the nodal grid's density and the subdomain's size.

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Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Localized Singular Boundary Method for Solving the Convection–diffusion Equation With Variable Velocity Field

Mužík

Bulko

2022

WIT Transactions on Engineering Sciences

Self Cite

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“…The localization principle is universally applicable, especially for methods emphasizing boundary points like the singular boundary method (SBM) or method of fundamental solutions (MFS). This principle defines a local solution region based solely on boundary points [8]. It mainly benefits the application of MFS, leading to the development of the local method of fundamental solutions (LMFS).…”

Section: Introductionmentioning

confidence: 99%

Stokes Equation Solution Using the Localized Method of Fundamental Solutions With a Global Basis

MUŽÍK,

CIGÁŇ

2023

Boundary Elements and Other Mesh Reduction Methods XLVI

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The paper focuses on deriving a local variant of the method of fundamental solutions (MFS) for the case of Stokes flow. Compared to the global and local basis variants, the local with global basis one leads to a sparse characteristic matrix as in fully localized variants but with a narrower system of equations and thus makes the solution of especially large-scale problems more efficient. It is also essential to keep the condition number of the characteristic matrix within reasonable bounds and remove the solution dependency on fictitious sources. A combination of MFS and finite collocation approach was used for the localization with a globally defined Stokeslet fundamental solution. The results of the particular local variant were compared on several examples, and the dependence of the solution on the density of the point network and the dimensions of the stencil used were also tested in the paper.

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Localized singular boundary method for solving Laplace and Helmholtz equations in arbitrary 2D domains

Wang

Chen

et al. 2021

Engineering Analysis with Boundary Elements

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Local singular boundary method for two-dimensional steady and unsteady potential flow

Cited by 9 publications

References 26 publications

Localized Singular Boundary Method for Solving the Convection–diffusion Equation With Variable Velocity Field

Localized Singular Boundary Method for Solving the Convection–diffusion Equation With Variable Velocity Field

Stokes Equation Solution Using the Localized Method of Fundamental Solutions With a Global Basis

Localized singular boundary method for solving Laplace and Helmholtz equations in arbitrary 2D domains

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