Some aspects relating to the accuracy of high-order panel methods

Dagan, A.; Jeans, Tiger L.; Cooper, Rodney H.

doi:10.1016/j.compfluid.2014.04.008

Cited by 2 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In light of the present analysis, it is clear that the spurious solution is a direct result of violating the Fredholm compatibility condition or, in other words, it is a direct consequence of the numerical error generated in the discretization process. However, none of the non-conservative schemes that have been employed here and in [13,17], comply with the compatibility constraint. Only the high-order schemes carry the lowest order of compatibility constraint violation which eventually has a minimal effect on the solution.…”

Section: Conservative Form and The Solvability Condition Of A Fredholmentioning

confidence: 93%

“…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%

“…Substituting (17) into the left-hand side of the above equation and employing the trapezoidal rule on the right-hand side, the total numerical error T e can be obtained (see [13]):…”

Section: Conservative Form and The Solvability Condition Of A Fredholmentioning

confidence: 99%

“…The foil geometry is now expressed by a third-order polynomial representing the foil geometry in each (j) interval with size h j (for detailed information, see [17]) 3 , while the distribution of the singularity strength γ along each element remains unchanged as in (8). Upon inserting the distribution of ξ , (9) takes the form:…”

Section: Higher-order Panels-periodic Cubic-spline Interpolationmentioning

confidence: 99%

“…The above approach requires considerably more programming effort and computer operations compared to the ''adding and subtracting'' approach (see Section 3.2). Further details regarding the method can be found in [17].…”

Section: Higher-order Panels-parabolic Lagrange Interpolationmentioning

confidence: 99%

See 4 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Conservative Form and The Solvability Condition Of A Fredholmentioning

confidence: 93%

“…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%

“…Substituting (17) into the left-hand side of the above equation and employing the trapezoidal rule on the right-hand side, the total numerical error T e can be obtained (see [13]):…”

Section: Conservative Form and The Solvability Condition Of A Fredholmentioning

confidence: 99%

Section: Higher-order Panels-periodic Cubic-spline Interpolationmentioning

confidence: 99%

Section: Higher-order Panels-parabolic Lagrange Interpolationmentioning

confidence: 99%

See 3 more Smart Citations