Title: B-Spline finite element solution of 1D contaminant transport equation along unsteady flow in saturated contaminant free porous media with general boundary conditions

Authors: Mansi S. Palav; Vikas H. Pradhan

Addresses: Department of Mathematics, SVNIT, Surat, Gujarat, 395007, India ' Department of Mathematics, SVNIT, Surat, Gujarat, 395007, India

Abstract: In the present paper, an analytical solution for 1D non-reactive contaminant transport in a homogeneous contaminant-free porous medium with time-dependent velocity has been modified by considering well-posedness of the problem in previous standard literature. The analytical solution has been considered by considering ill-posedness of the problem where the obtained analytical solution does not depend continuously on time and does not satisfy the initial condition. The analytical solution has been obtained by considering the general boundary condition which preserve the compatibility of the boundary and initial condition. Laplace transform technique has been applied to obtain modified analytical solution and compared with the previous analytical solution for ill posed-ness of the problem. The numerical solution is also obtained using Quadratic B-Spline finite element method (QBSFEM) and compared with obtained analytical solution and error analysis is also done.

Keywords: well-posed; general boundary condition; B-spline; FEM; finite element method.

DOI: 10.1504/IJCSM.2024.143212

International Journal of Computing Science and Mathematics, 2024 Vol.20 No.4, pp.353 - 370

Received: 07 Mar 2024
Accepted: 19 Oct 2024
Published online: 09 Dec 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article