• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.4
• /
• pp.301-327
• /
• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• Advances in concrete construction
• /
• v.10 no.4
• /
• pp.357-367
• /
• 2020

The impulse of this paper is to examine the influence of unsteady flow comprising of Eyring-Powell nanofluid over a stretched surface. This work aims to explore efficient transfer of heat in Eyring-Powell nanofluid with bio-convection. Nanofluids possess significant features that have aroused various investigators because of their utilization in industrial and nanotechnology. The influence of including motile microorganism is to stabilize the nanoparticle suspensions develop by the mixed influence of magnetic field and buoyancy force. This research paper reveals the detailed information about the linearly compressed Magnetohydrodynamics boundary layer flux of two dimensional Eyring-Powell nanofluid through disposed surface area due to the existence of microorganism with inclusion the influence of non- linear thermal radiation, energy activation and bio-convection. The liquid is likely to allow conduction and thickness of the liquid is supposed to show variation exponentially. By using appropriate similarity type transforms, the nonlinear PDE's are converted into dimensionless ODE's. The results of ODE's are finally concluded by employing (HAM) Homotopy Analysis approach. The influence of relevant parameters on concentration, temperature, velocity and motile microorganism density are studied by the use of graphs and tables. We acquire skin friction, local Nusselt and motil microorganism number for various parameters.