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In this paper, FD formulations in cylindrical coordinates are used to model the field radiated, by a circular source, in fluid and solid media.

The stability of the used schemes is controlled by a proper choice of time and space steps. Absorbing boundary conditions are introduced to satisfy the assumption of a propagation in a half space medium. In order to minimize the CPU time, calculations are limited for regions disturbed by the propagating ultrasonic pulse then the calculus zone is incremented.

Some numerical results are presented to illustrate the effect of the medium nature, source vibration profiles and eventually the presence of targets in the acoustic field. A spatio-temporal description of the diffraction phenomena is given. The radiated field is interpreted in terms of plane and edge waves. For solid media, this interpretation allows the determination of the arrival times which are compared with those numerically predicted. Numerical results corresponding to fluid media are compared to those obtained by the Impulse Response Method. The good agreement obtained justifies the choice of the FDM for the modeling of the wave propagation problems.

This paper analyzes the interaction of high Rayleigh number flow with conjugate heat transfer. The two-relaxation time lattice Boltzmann is used as a turbulent buoyancy-driven flow solver whereas the implicit finite difference technique is applied as a heat transfer solver. An in-house numerical code is developed and successfully validated on typical CFD problems. The impact of the Biot number, heat diffusivity ratio and the Rayleigh number on turbulent fluid flow and heat transfer patterns is studied. It is revealed that the thermally-conductive walls of finite thickness reduce the heat transfer rate. The temperature of the cooled wall slightly depends on the value of the buoyancy force. The heat diffusivity ratio has a significant effect on thermal and flow behavior. The Biot number significantly affects the mean Nusselt number at the right solid–fluid interface whereas the mean Nusselt number at the left interface is almost insensible to the Biot number variation.

This paper provides an analysis of the numerical performance of a hybrid computational fluid dynamics (CFD) solver for 3D natural convection. We propose to use the lattice Boltzmann equations with the two-relaxation time approximation for the fluid flow, whereas thermodynamics is described by the macroscopic energy equation with the finite difference solution. An in-house parallel graphics processing unit (GPU) code is written in MATLAB. The execution time of every single step of the algorithm is studied. It is found that the explicit finite difference scheme is not as stable as the implicit one for high Rayleigh numbers. The most time-consuming steps are energy and collide, while stream, boundary conditions, and macroscopic parameters recovery are executed in no time, despite the grid size under consideration. GPU code is more than 30 times faster than a typical low-end central processing unit-based code. The proposed hybrid model can be used for real-time simulation of physical systems under laminar flow behavior and on mid-range segment GPUs.

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.