Conservative form and spurious solutions in moving boundary elements methods

Dagan, A.; Jeans, Tiger L.

doi:10.1016/j.compfluid.2014.03.029

Cited by 2 publications

(18 citation statements)

References 17 publications

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“…63-64], [11,12]. We are also going to mention briefly the piecewise-linear singularity-sheet distribution as appears in more detail in [13,17,14,23,24], [1, Section 10].…”

Section: Numerical Algorithmsmentioning

confidence: 99%

“…It has been pointed out in [13] that low-order accurate schemes (such as the piecewise-linear singularity-sheet distribution) generate spurious solutions and are, therefore, incapable of producing a reliable solution. To strengthen this point in light of the Fredholm compatibility condition (we will elaborate upon this in the next section), we will briefly explain the derivation of the numerical algorithms that are based upon panel methods.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

“…Therefore, by adding and subtracting the integrand at the singularity point ([2, pp. 63-64], [13,11,12]), the following expression is obtained:…”

Section: Adding and Subtracting The Singularitymentioning

confidence: 99%

“…Eq. (7) has been employed in boundary element solvers [14], including moving boundaries [23,24] and further details regarding the method of deriving (7) can be found in [13].…”

Section: Piecewise-linear Singularity-sheet Distributionmentioning

confidence: 99%

“…However, in this study we will only examine the high-order panel methods in the case where Q = 0 (see also [13]). By imposing a continuous normal velocity V n = V − n across the body interface, the following Fredholm integral equations are obtained:…”

Section: Introductionmentioning

confidence: 99%

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Spurious solutions in a Fredholm integral equation of the second kind with a Cauchy kernel

Dagan

Jeans

Cooper

2015

Journal of Computational and Applied Mathematics

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Fredholm integral equation of the second kind Cauchy integral Spurious solution Truncation error a b s t r a c tIn this study, we have addressed the appearance of a spurious solution generated when employing low-order accurate schemes for a Fredholm integral equation of the second kind in potential-flow problems, which is highly relevant to moving boundary problems. It is shown that the numerical error resulting from discretization of the Cauchy integral violates the Fredholm solvability condition, which is related to the conservation of the circulation, at the discretization level. In other words, the numerical error is not orthogonal to the homogeneous solution of the adjoint equation and therefore does not comply with the Fredholm compatibility condition. The Fredholm compatibility condition appears to be the total accumulated truncation error requiring circulation preservation at the discretized level. Therefore, in order to obtain a solution, the truncation-error distribution must be redistributed to comply with the requirements imposed by the compatibility constraint. The outcome of violating the solvability constraint is the spurious solution and it seems to be controlled by the numerical diffusion/dispersion terms in the numerical scheme.

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“…63-64], [11,12]. We are also going to mention briefly the piecewise-linear singularity-sheet distribution as appears in more detail in [13,17,14,23,24], [1, Section 10].…”

Section: Numerical Algorithmsmentioning

confidence: 99%

Section: Numerical Algorithmsmentioning

confidence: 99%

“…Therefore, by adding and subtracting the integrand at the singularity point ([2, pp. 63-64], [13,11,12]), the following expression is obtained:…”

Section: Adding and Subtracting The Singularitymentioning

confidence: 99%

“…Eq. (7) has been employed in boundary element solvers [14], including moving boundaries [23,24] and further details regarding the method of deriving (7) can be found in [13].…”

Section: Piecewise-linear Singularity-sheet Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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