CV dual reciprocity BEM for transient flow in blocky systems with singular points and lines of discontinuities

The advantages of the complex variable (CV) and dual reciprocity method (DRM) are combined to effectively solve plane problems for heat (fluid, charge) flow in blocky systems with potential, flux, and/or conductivity discontinuity at contacts and with singular points such as crack tips, common apexes of structural elements and thin inclusions. We establish that in the problems considered it is reasonable to (i) distinguish the holomorphic “quasi-steady” part of the solution, (ii) use Gauss-type radial basis functions (RBF) to simplify further the employment of a found solution of a potential problem for solving thermo- (poro-) elastic problems, (iii) locate the centers of RBF outside of the contour of integration, (iv) account for the sensitivity of the solution to the distance between the centers of RBF by taking the normalized distance as d = t * / 1 . 2 8 to have the accuracy of one percent at a normalized time t*, and account for the sensitivity to the scaling parameter asc by taking it within the range 1.6d<asc<8d to avoid growing inaccuracy of the solution for small values of asc (asc<1.6d) and growing instability for large values of asc (asc>8d), and (v) use the solution of the ordinary differential equations (ODE) with respect to approximation parameters rather than with respect to the temperature at the centers of RBF. Numerical tests and examples illustrate the accuracy and abilities of the developed technique.