Modified B-spline Differential Quadrature Method Research Articles

Numerical simulation of interface tracking between two immiscible micropolar and dusty fluids

The development of the interfacetracking between two immiscible liquids is one of the most challenging problems in fluid dynamics. The simulation of the lubrication process, oil extraction, and the physicochemical mechanism that govern the behaviour of the uncertain conduct of interface is a key element in “gas-oil” or “oil–water” natural gas-oil reservoirs systems and should be tracked for optimal recovery. Motivated by the interface evolution process, in this article, an unsteady flow of two immiscible Eringen micropolar and Dusty (fluid-particle suspension) fluids is considered through a horizontal channel and the functioning of the interface is analysed. Although the channel wall is hyper-stick and no-slip, it is believed that the fluid–fluid interface is unsteady and can also be deformed from one location to another; thus, the single momentum equation is coupled for monitoring the interface profiles using the VOF (Volume of fluid) technique. The modelled coupled- partial differential equations are numerically solved by the modified B-spline differential quadrature method. The interface profile under the influence of different parameters, i.e., Froude, Capillary, wave and Reynolds number, amplitude, the ratio of viscosities, and time is analysed. Three applied pressure gradients namely constant Ge = 10, periodic Ge = 10Sin(t), and decaying Ge = e-t are considered with various constant values of other hydrodynamic parameters. It's been noted that thetopologydevelops with time asthe pulsing pattern repeats quicker for a longer period before becoming stable. The flow's qualitative characteristics remain preserved, the interface begins to move vertically as the amplitude is elevated. A higher interfacial drift is seen in the applied periodic pressure gradient case as compared to the constant and decaying pressure gradient scenario. The tracking does take high time to be stable in the presence of the micropolar parameter with all three applied pressure gradient cases.

A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method

The present paper uses a relatively new approach and methodology to solve second order two dimensional hyperbolic telegraph equation numerically. We use modified cubic B-spline basis functions based differential quadrature method for space discretization that reduces the problem into an amenable system of ordinary differential equations. The resulting system of ODEs in time subsequently have been solved by SSP-RK43 scheme. Stability of the scheme is studied using matrix stability analysis and found to be stable. The efficacy of proposed approach has been confirmed with seven numerical experiments, where comparison is made with some earlier work. It is clear that the results obtained are acceptable and are in good agreement with earlier studies. However, we obtain these results in much less CPU time. The method is very simple, efficient and produces very accurate numerical results in considerably smaller number of nodes and hence saves computational effort.