DRBEM Solution of Singularly Perturbed Magnetohydrodynamic Duct Flow using Parallel Computing

I. Workshop on Applied Mathematics and Statistics, İzmir, Türkiye, 10 Mayıs 2025, ss.12, (Özet Bildiri)

Yayın Türü: Bildiri / Özet Bildiri
Basıldığı Şehir: İzmir
Basıldığı Ülke: Türkiye
Sayfa Sayıları: ss.12
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

This study focuses on the numerical solution of singularly perturbed magnetohydrodynamic (MHD) flow in a square duct for no-slip and insulted walls at high Hartmann numbers (Ha). The flow is steady, laminar, fully developed, and occurs in an incompressible, viscous, electrically conducting fluid, driven by a pressure gradient along a long pipe of square cross-section (duct). The governing equations of the MHD flow are of convection-diffusion type and are coupled through the velocity field V (x, y) and the induced magnetic field B(x, y). When a strong external magnetic field is applied horizontally, Hartmann number (Ha) increases significantly, enhancing the convection effects in the system. This leads to convection-dominated behavior in the coupled equations, with the diffusion terms becoming negligible. As a result, the system becomes a singularly perturbed problem characterized by thin boundary layers near the walls and it is very difficult to capture the flow behavior near the walls. To address this problem numerically, parallel computation of the Dual Reciprocity Boundary Element Method (DRBEM) is utilized in conjunction with a Shishkin mesh, which adapts the number of nodes taken on the boundary and Ha. The incorporation of parallel computing is essential in this framework, as it not only significantly reduces the computational time but also enables us to reach extremely large Hartmann numbers up to 1500. The numerical results demonstrate that the expected features of MHD duct flow emerge clearly and accurate solutions for both V (x, y) and B(x, y) can be obtained.