caa a22 4500 475839951 CHVBK 20180406123858.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1004666000020 doi (NATIONALLICENCE)springer-10.1023/A:1004666000020 Suh J.-C Department of Naval Architecture and Ocean Engineering, Seoul National University, RIMSE, 151-742, Seoul, Korea aut The evaluation of the Biot-Savart integral [Elektronische Daten] [J.-C. Suh] A computational method is described for evaluating the Biot-Savart integral. The approach emphasizes the transformation of the involved integrand into suitable forms, from which integral theorems can be used to reduce the volume integral into line integrals. This method is applied to the case where the density of vorticity (current) distributed over a volumetric element bounded by planar surfaces (straight lines in two-dimensional) is constant and/or linear. The resulting expressions for the volume integral involve closed-form expressions for line integrals along the edges of the element. The evaluation of the line integrals is treated independently for each of the edges as opposed to direct numerical integration. The closed-form formulas are expressed in terms of geometric parameters of the element edges. The versatility of the proposed scheme is demonstrated by applying it to two examples: (i) two-dimensional lid-driven cavity flows; (ii) a magnetic field induced by a toroidal tokamak coil. A systematic extension to the general cases where the vorticity distribution is of higher-order polynomial form is also presented. Kluwer Academic Publishers, 2000 Biot-Savart law nationallicence linearly varying density nationallicence transformation of integrands nationallicence contour integrals nationallicence closed-form expressions nationallicence Journal of Engineering Mathematics Kluwer Academic Publishers 37/4(2000-05-01), 375-395 0022-0833 37:4<375 2000 37 10665 https://doi.org/10.1023/A:1004666000020 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004666000020 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Suh J.-C Department of Naval Architecture and Ocean Engineering, Seoul National University, RIMSE, 151-742, Seoul, Korea aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 37/4(2000-05-01), 375-395 0022-0833 37:4<375 2000 37 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer