Computational Fluid Dynamics, Fluid Mechanics - Essay Sample

Introduction

The computational fluid dynamics refers to the branch of the fluid mechanics which uses the data structures as well as the numerical analyses to analyses as well as solve the problems which involve the flow of the fluid. In this case, there is the use of computers in the performance of calculations which are required to act as simulations of the free flows of the fluid in a stream, as well as the interactions of such flowing fluids with the surfaces they come in contacts with, as defined by the conditions of the boundaries. There is thus the attainment of a better solution in the event the high-speed supercomputers are put into use. In the process, there is also the use of such supercomputers in the solution of large scale as well as quite complex mathematical problems involving the fluid. Besides, there is the use of software that helps in the improvement of accuracy as well as the speed of the complex simulators which can involve such aspects as turbulent or even transonic flows. In this case, the validation of such software employed in complex calculations of fluid properties, and more especially during their flows, are done using the experimentation apparatus such as the wind tunnel, alongside the comparison with the solutions obtained where there was the computation of a particular problem of the same nature in the past using the same software. There is finally the final validation of such software following the use of large-scale data, where reasonable results are obtained, which can include flight tests. The software also has mathematical models which enable the establishment of the complex computations involving the fluid mechanics. The choice of such mathematical models is influenced by their preferability in terms of accuracy to the results obtained, ease of use, flexibility, and even their applicability in the solution of different problems involving fluid mechanics. Such models are as brought out subsequently, with their explanations as well as the justification for their use.

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First, there is a mathematical model referred to as the Eulerian model. It is the model which primarily bases on the numerical solution of the atmospheric transport equation (Tu, & Yeoh, 2013). In this case, there is the atmospheric transport equation is a second order equation mathematically. It has the solutions to the fluid flow properties with the appropriate initial as well as the boundary conditions that are aimed to provide the spatiotemporal evolution of the concentration. The model has been chosen because of its richness in terms of the ability to serve a wide variety of problems related to fluid mechanics, using its wide range of methods of solving mathematical problems. One of such methods is the 'method of lines.' It is considered as the most powerful as well as the most common method in the solution of fluid mathematical problems. It is because of its ability to yield results which are accurate to the highest order, as well as the ease application of the method in the run towards the solution of mathematical problems. It consists of two steps. The first one is the spatial discretization and the second one is the temporal integration of all the derived ordinary differential equations. For the case of the spatial discretization of PDE, which is also referred to as the atmospheric transport equation. It is performed in a mesh, also known as a mesh. It reduces the system of PDE in the ordinary differential equation in its one independent variable, the tie. As a result, the system of the ordinary differential equation can be solved as the initial problem. There are also various software tools as well as the methods which can be used along the above method in the solution of fluid dynamics problem, thus raising the probability of the accuracy of the results obtained in the long run. Such, therefore, serve to justify the reason for the choice of the Eulerian method in the solution of fluid dynamics problems at hand.

Further justifying the choice of the Eulerian model, there is the use of a successful case example where it has been and is still applicable. In this regard, it has been the evident basis of almost all the air pollution models being in a system of spatial differential equations, that contains several terms. They aid in the description of diverse chemical and physical processes which are associated with the transport of air pollution. There is efficient numerical integration of the transport equations during computations. It thus leads to an eventual approach of the fluid problem from all angles, leading to the solution of the problem as required. Also, the model has had its splitting been successfully applied in the Navier - Stokes equations.

Additionally, there is the choice of the Lagrangian model in the solution of fluid mechanics problems under computational fluid dynamics. Such problems mainly concern the fluid flow involving pollution particles in the atmosphere. It operates based on the idea that there are the particles which move through the atmosphere along the trajectories by the turbulent effects, the buoyancy, as well as the wind fields. In this regard, there shall then be the computation of such problems where there is the obtaining of ordinary differential equations as opposed to the partial differential equations. The ordinary differential equations are easy to calculate, hence selection of the Lagrangian model in the computational fluid flows where there is the need to solve certain problems in the long run. In the computation, there is usually an eventual stochastic estimation which serves to display the concentration fields. The functioning order of the model is that it can estimate the fluid particle as a one moving point which drafts on a particular surface or the eventual large distributions of particles which move together hence facilitating the estimation of the concentration of the trajectory models of the fluid particles.

Besides, there hare the turbulence models who are chosen for mathematical calculations of the fluid mechanics in the min the computational fluid dynamics. They are chosen because of some favorable reasons in terms of their applicability in the tasks specialized for. In this regard, they are employed for the case of the calculations involving the turbulent form of fluids because of the abilities of the model to facilitate the prediction of the quantities of interest n the long run. Such quantities can involve the velocity of the fluids (Shaari, & Awang, 2015). Thus, the model is advantageous for prediction of fluid properties which can thus be used in decision making on whether they should be applied for particular activities in the engineering arena. Also, such predictions can be utilized in the engineering design of the systems that are to be applied in different areas, including the designing of brake fluid systems.

For the case of turbulent flows of fluids, there is a wide range of length scales as well as the complexities of the phenomena which are involved in the turbulent flow of the fluids. They thus make most of the modeling processes to be quite costly in the long run. In this regard, there is the solution, whereby there is the need to resolve all the scales involved in the operations beyond what is possible in terms of computation, as defined by the turbulent model at hand. It makes the resolutions to employ the variables involved in turbulent flows in an eased manners thus simplifying the computational work in the long run. One of such approaches can involve the creation of numerical models under the turbulent models, which will in the end aid in the approximation of the unresolved phenomena in the long run.

Moreover, the turbulent model has a variety of methods which can be employed in the resolution of the fluid mechanic's problems. They range in their computational costs, complexity and ease of use, thus making it possible to select the method only applicable in certain areas as dictated by the available expenses and the need of convenience in terms of ease of use. The resolution using more turbulent scales brings about finer details hence its costly nature. They also range in terms of accuracy, hence making it possible for the prediction of the level of accuracy of the method employed. They include the Reynolds - averaged Navier - Stokes method which is projected to be less accurate, the vortex method which is a technique used in the simulations involving turbulent flows.

References

Shaari, K. Z. K., & Awang, M. (2015). Engineering Applications of Computational Fluid Dynamics.

Tu, J., Liu, C., & Yeoh, G. H. (2013). Computational fluid dynamics: A practical approach, second edition. Waltham, Mass: Butterworth-Heinemann.