<span style="font-family:Verdana;">The term</span> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;&...<span style="font-family:Verdana;">The term</span> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">“</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hydraulics</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">”</span></span></span></span><span><span><span><span style="font-family:;" "=""> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is </span></span></span></span><span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">concerned with the conveyance of water that can consist of very simple processes to complex physical processes, such as flow </span><span style="font-family:Verdana;">in open rivers, flow in pipes, </span></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">flow of nutrients/sediments, </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">flow of</span></span></span></span><span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> groundwater to sea waves. The study of hydraulics is primarily a mixture of theory </span><span style="font-family:Verdana;">and experiments. Computational hydraulics is very helpful to quantify and </span><span style="font-family:Verdana;">predict flow nature and behavior. </span></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">mathematical model is </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">backbone of the computational hydraulics that consist</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span></span><span><span><span><span style="font-family:;" "=""> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">of </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">simple to complex mathematical equations with linear and/or non-linear terms and ordinary or partial differential equations. Analytical solution </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">to</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> th</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ese</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> mathematical equations is not feasible in the majority of cases. In these consequences, mathematical models are solved using different numerical techniques and associated schemes. In this manuscript</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> we aim to review hydraulic principles along with their mathematical equations. Then we aim to learn some commonly used numerical technique</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> to solve different types of differential equations related to hydraulics. Among them</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the Finite Difference Method (FDM), Finite Element Method (FEM) and Finite Volume Method (FVM) have been discussed along with their use in real-life applications in the context of water resources engineering.</span></span></span></span>展开更多
Understanding, quantifying, and forecasting water flow and its behavior in environment is made possible by the use of computational hydraulics in conjunction with numerical models, which is one of the most powerful to...Understanding, quantifying, and forecasting water flow and its behavior in environment is made possible by the use of computational hydraulics in conjunction with numerical models, which is one of the most powerful tools currently available. It is made up of simple to complex mathematical equations having linear and/or nonlinear elements, as well as ordinary and partial differential equations, and it is used to solve problems in many areas. In the vast majority of cases, it is not useful to reach analytical solutions to these mathematical equations using conventional methods. In these settings, mathematical models are solved by employing a variety of numerical algorithms and associated schemes. As a result, in this manuscript, we will cover the most fundamental numerical approach, the Finite Difference Method (FDM), in order to reformulate the governing equations for water and sediment flow from a system of partial differential equations to a system of linear equations. As part of our analysis into the inner workings of a computer program known as MIKE 21C, we will attempt to gain a better understanding of the hydrodynamic processes that take place in major rivers in Bangladesh. In addition to that, we will go over some of the most commonly used morphological studies that have been conducted on Bangladesh’s major rivers, including morphological solutions that have been developed in response to water supply concerns.展开更多
文摘<span style="font-family:Verdana;">The term</span> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">“</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hydraulics</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">”</span></span></span></span><span><span><span><span style="font-family:;" "=""> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is </span></span></span></span><span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">concerned with the conveyance of water that can consist of very simple processes to complex physical processes, such as flow </span><span style="font-family:Verdana;">in open rivers, flow in pipes, </span></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">flow of nutrients/sediments, </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">flow of</span></span></span></span><span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> groundwater to sea waves. The study of hydraulics is primarily a mixture of theory </span><span style="font-family:Verdana;">and experiments. Computational hydraulics is very helpful to quantify and </span><span style="font-family:Verdana;">predict flow nature and behavior. </span></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">mathematical model is </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">backbone of the computational hydraulics that consist</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span></span><span><span><span><span style="font-family:;" "=""> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">of </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">simple to complex mathematical equations with linear and/or non-linear terms and ordinary or partial differential equations. Analytical solution </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">to</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> th</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ese</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> mathematical equations is not feasible in the majority of cases. In these consequences, mathematical models are solved using different numerical techniques and associated schemes. In this manuscript</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> we aim to review hydraulic principles along with their mathematical equations. Then we aim to learn some commonly used numerical technique</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> to solve different types of differential equations related to hydraulics. Among them</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the Finite Difference Method (FDM), Finite Element Method (FEM) and Finite Volume Method (FVM) have been discussed along with their use in real-life applications in the context of water resources engineering.</span></span></span></span>
文摘Understanding, quantifying, and forecasting water flow and its behavior in environment is made possible by the use of computational hydraulics in conjunction with numerical models, which is one of the most powerful tools currently available. It is made up of simple to complex mathematical equations having linear and/or nonlinear elements, as well as ordinary and partial differential equations, and it is used to solve problems in many areas. In the vast majority of cases, it is not useful to reach analytical solutions to these mathematical equations using conventional methods. In these settings, mathematical models are solved by employing a variety of numerical algorithms and associated schemes. As a result, in this manuscript, we will cover the most fundamental numerical approach, the Finite Difference Method (FDM), in order to reformulate the governing equations for water and sediment flow from a system of partial differential equations to a system of linear equations. As part of our analysis into the inner workings of a computer program known as MIKE 21C, we will attempt to gain a better understanding of the hydrodynamic processes that take place in major rivers in Bangladesh. In addition to that, we will go over some of the most commonly used morphological studies that have been conducted on Bangladesh’s major rivers, including morphological solutions that have been developed in response to water supply concerns.