The Treatment of Boundary Singularities in Axially Symmetric Problems Containing Discs

Crank, John P.; Furzeland, R.M.

doi:10.1093/imamat/20.3.355

Cited by 45 publications

(23 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is however better to allow diffusion in this region by using both second spatial derivatives, invoking (4c) only in the sense of symmetry about the axis. The 1/R problem is handled as suggested by Crank and Furzeland [12], using the Maclaurin formula…”

Section: (R Z) Space Simulationsmentioning

confidence: 99%

“…It was noticed early that the ultramicrodisk and -band have an edge problem of a current density singularity, both experimentally [7] and theoretically or by simulation [1,3,[8][9][10][11][12][13][14][15][16][17][18][19][20][21], and the singularity is implicit in Saito's 1968 work [22], which is the source for the steady state value of the current at a disk (although Saito did not remark on the edge effect). The edge effect led Gavaghan [23] to design a mesh for the simulation of the disk that used very unequal intervals, concentrated not only near the disk surface but also at its edge.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum grid digital simulation of chronoamperometry at a disk electrode

Britz

Østerby

Strutwolf

2012

Electrochimica Acta

View full text Add to dashboard Cite

a b s t r a c tWe seek to find the best ways to achieve a minimum grid with a given target accuracy in the computed current in the simulation of a diffusion limited chronoamperometric experiment at an ultramicrodisk electrode. We present some results for direct discretisation on the cylindrical geometry in (R, Z) space and in transformed coordinates (Â, ), comparing four commonly used transformations. In all cases, the use of multi-point spatial derivative approximations are explored to find an optimum. Orthogonal collocation is studied in the two dimensions, and found less efficient than an evenly divided grid and smaller multi-point approximations. The eigenvalue-eigenvector method is studied and found to be relatively inefficient but was useful in providing some information on error waves seen with three of the four transformations used. These error waves are not due to an error propagation, a fact that became clear from the eigenvalue-eigenvector method, which reproduced the waves.

show abstract

Section: (R Z) Space Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum grid digital simulation of chronoamperometry at a disk electrode

Britz

Østerby

Strutwolf

2012

Electrochimica Acta

View full text Add to dashboard Cite

show abstract

“…Such an approximation has been used in many numerical algorithms. In Crank and Furzeland [13], for instance, they presented a modified finite-difference method which eliminates inaccuracies that occur in the standard numerical solution near singularities. The approximation has also been used by Harley and Momoniat [19] .T h i s difference scheme (15), including the initial difference condition (14), form a system of equations which are to be solved iteratively.…”

Section: Crank-nicolson Implicit Schemementioning

confidence: 99%

Numerical Simulation of the Frank-Kamenetskii PDE: GPU vs. CPU Computing

Harley¹

2012

MATLAB - A Fundamental Tool for Scientific Computing and Engineering Applications - Volume 3

View full text Add to dashboard Cite

“…The case k > 0 represents the family of axially symmetric problems discussed in Crank and Furzeland [11]. The case k < 0 represents axially symmetric flow problems where U is the stream function.…”

Section: N T H E P a R A B O L I C C A S E T H I S T R A N S F O R mentioning

confidence: 99%

“…g . f o r t h e e v a l u a t i o n o f t h e f l u x in diffusion problems, Crank and Furzeland [11] or for the m e a s u r e m e n t o f c a p a c i t a n c e i n p o t e n t i a l p r o b l e m s , D u n c a n [ 1 3 ] . L a r g e e r r o r s 17.…”

Section: B O T H T H E P R O P O S E D Me T H O D a N D T H E A L T Ementioning

confidence: 99%