In this work, the strategy for numerical solutions in transport processes is investigated. Permeation problems can be solved analytically or numerically by means of Finite Difference Method (FDM), while choosing Euler forward explicit backwards implicit formalism. The first method easiest and most commonly used, not yet well established needs further development. Hereafter, a possible solution ...

Many mathematical formulations of physical phenomena contain integro-differential equations. In this paper a numerical method is developed to solve the convection-diffusion integro-differential equations with a weakly singular kernel using the cubic B-spline collocation method. These equations occur in many applications such as in the transport of air and ground water pollutants, oil reservoir ...

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The converg...

Koren, B. and P.W. Hemker, Damped, direction-dependent multigrid for hypersonic flow computations, Applied Numerical Mathematics 7 (1991) 309-328. A nonlinear multigrid technique with improved robustness is developed for the solution of the steady Euler equations. The system of nonlinear equations is discretized by an upwind finite volume method. Collective symmetric point Gauss-Seidel relaxati...

The present numerical attempt deals the sway to transfer of heat and mass characteristics on the time-dependent hydromagnetic boundary layer flow of a viscous fluid over an exponentially inclined preamble stretching. Furthermore, the role of viscous heating, thermal radiation, uneven energy gain or loss, velocity slip, thermal slip and solutal slips are depicted. The prevailing time-dependent P...

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The converg...

The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

Stochastic collocation method has proved to be an efficient method and been widely applied to solve various partial differential equations with random input data, including NavierStokes equations. However, up to now, rigorous convergence analyses are limited to linear elliptic and parabolic equations; its performance for Navier-Stokes equations was demonstrated mostly by numerical experiments. ...

In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We study an implicit-explicit (IMEX) time discretization in which the convection is explicit while the relaxation term is implicit to ove...

A preconditioned five-equation two-phase model coupled with an interface sharpening technique is introduced for simulation of a wide range of multiphase flows with both high and low Mach regimes. Harten-Lax-van Leer-Contact (HLLC) Riemann solver is implemented for solving the discretized equations while tangent of hyperbola for interface capturing (THINC) interface sharpening method is applied ...