Boundary integral solution of MHD pipe flow

The process of modeling of physical systems into mathematical problems as a set ofeither algebraic or differential equations is illustrated schematically. The need for com-putational methods and related problems in numerical solutions are discussed givingsome challenging physical models. Components of a numerical solution method isshown with several discretization methods.As a special application in fluid dynamics, the boundary integral solution ofmagnetohydrodynamic (MHD) pipe flow is presented. The MHD flow problem ina circular pipe defined by convection-diffusion equations is coupled with an exteriorNeumann or Dirichlet magnetic problem defined by the Laplace equation through thecoupled boundary conditions on the pipe wall. A semi-analytical solution method isprovided in the sense that, the theoretically obtained three boundary integral equationsfor interior Dirichlet and exterior Dirichlet or Neumann problems are solved numericallyby using collocating points on the pipe wall. The solution is simulated for several valuesof problem parameters to demonstrate the well-known MHD characteristics