Abstarct: ‎Abstract In incompressible flows, due to the constant density, the term of the time derivative of the density is removed from the continuity equation, and as a result, the relations between the continuity and momentum equations are lost, and these equations become independent. Also, it will not be possible to use time marching methods to solve the governing equations. This problem is the most important challenge in solving the governing equations of incompressible flows. One of preconditioning the governing equations and, as a result, equating the eigenvalues of the system of governing equations. Of course, this approach, in addition to reducing the difficulty of the system of governing equations from the mathematical aspects by coupling the continuity and momentum equations, also provides the possibility of using time marching methods to solve the equations numerically and by choosing the appropriate time step, it also increases the convergence speed of the numerical solution. Therefore, designing or selecting a suitable preconditioning method with both the speed of convergence and the appropriate accuracy and efficiency in different physica l conditions of a problem is considered one of the important challenges of the preconditioning strategies. Another important challenge in computational fluid dynamics is the numerical solution of flows in an infinite physical space. Numerical simulation of this type of flow should be carried out in a limited computational space, and for this limitation, especially in far-field boundaries, a hypothetical or artificial boundary should be defined at a suitable distance from the object, and a proper boundary condition should be considered for it. Choosing the place of this hypothetical boundary and how to determine the flow quantities on this boundary will significantly impact the efficiency and accuracy of the results of the numerical algorithm. Numerical errors, which are the inseparable nature of numerical methods, begin to grow with the beginning of the numerical solution process and are produced and propagated in the form of acoustic and pressure waves within the solution field. Suppose common reflective boundary conditions are used in the artificial boundaries, such as keeping the pressure constant at the outlet boundary and determining the velocity field with the aid of interpolation from inside the field (in which the propagation of waves is not allowed), the waves after reaching the far-field boundary. In that case, it reflects into the solution field, and by contaminating the solution field, it slows down the convergence speed of the numerical simulation. Nowadays, using the new approach of non-reflective boundary conditions in the artificial boundary, researchers have prevented the reflection of waves into the field of numerical solution, and as a result, they greatly increase the accuracy, efficiency, and convergence speed of numerical simulation. In this thesis‎‎, to speed up the numerical solution of incompressible flows, characteristic boundary conditions (which are a new type of non-reflective boundary conditions) are extracted for far-field artificial boundaries and with the unique locally power-law preconditioning method of (which is considered an innovative and smart preconditioning method) to be combined. Also, this method is applied on a finite volume method, and finally, this developed combined method is used in the numerical simulation of steady and unsteady incompressible flows. In the locally power-law preconditioning method, the preconditioning matrix is acquired from a power relation and using local sensors of the velocity field in each time step. The governing equations are integrated with the aid of the cell-centered finite volume method, and a dual-time algorithm is used to solve unsteady flows. The preconditioned governing equations in the Cartesian coordinate system are transferred from the physical space to the computational space to use characteristic non-reflective boundary conditions at the boundaries. It should be mentioned that this transfer is implemented only at the boundaries to achieve the characteristic equations. Then, the characteristic and diagonalized forms of the governing equations are extracted. In the following, these equations are integrated along the characteristic lines to determine the flow characteristics on the far-field boundaries. After the integration equations and the corresponding characteristic variables are determined mathematically, they are applied as appropriate boundary conditions in the incompressible flow solver. A program has been written in C ++ programming language to evaluate the proposed combined-developmental method to simulate incompressible flows. At first, the numerical simulation results of steady and unsteady turbulent incompressible flow have been investigated using the locally power-law preconditioning method using common boundary conditions. Then, in the following, the results acquired from the locally power-law preconditioning method using characteristic non-reflective boundary conditions in the simulation of incompressible flows in a wide range of Reynolds numbers (from 500 to 5.25×‎106‎) and angles of attack (from 0 to 20 degrees) around three airfoils of NACA0012, ONERA, and S809 is provided. Also, a comprehensive sensitivity study (including investigating the effects of the CFL of acoustic and pressure waves within the solution field. Suppose common reflective boundary conditions are used in the artificial boundaries, such as keeping the pressure constant at the outlet boundary and determining the velocity field with the aid of interpolation from inside the field (in which the propagation of waves is not allowed), the waves after reaching the far-field boundary. In that case, it reflects into the solution field, and by contaminating the solution field, it slows down the convergence speed of the numerical simulation. Nowadays, using the new approach of non-reflective boundary conditions in the artificial boundary, researchers have prevented the reflection of waves into the field of numerical solution, and as a result, they greatly increase the accuracy, efficiency, and convergence speed of numerical simulation. In this thesis‎‎, to speed up the numerical solution of incompressible flows, characteristic boundary conditions (which are a new type of non-reflective boundary conditions) are extracted for far-field artificial boundaries and with the unique locally power-law preconditioning method of (which is considered an innovative and smart preconditioning method) to be combined. Also, this method is applied on a finite volume method, and finally, this developed combined method is used in the numerical simulation of steady and unsteady incompressible flows. In the locally power-law preconditioning method, the preconditioning matrix is acquired from a power relation and using local sensors of the velocity field in each time step. The governing equations are integrated with the aid of the cell-centered finite volume method, and a dual-time algorithm is used to solve unsteady flows. The preconditioned governing equations in the Cartesian coordinate system are transferred from the physical space to the computational space to use characteristic non-reflective boundary conditions at the boundaries. It should be mentioned that this transfer is implemented only at the boundaries to achieve the characteristic equations. Then, the characteristic and diagonalized forms of the governing equations are extracted. In the following, these equations are integrated along the characteristic lines to determine the flow characteristics on the far-field boundaries. After the integration equations and the corresponding characteristic variables are determined mathematically, they are applied as appropriate boundary conditions in the incompressible flow solver. A program has been written in C ++ programming language to evaluate the proposed combined-developmental method to simulate incompressible flows. At first, the numerical simulation results of steady and unsteady turbulent incompressible flow have been investigated using the locally power-law preconditioning method using common boundary conditions. Then, in the following, the results acquired from the locally power-law preconditioning method using characteristic non-reflective boundary conditions in the simulation of incompressible flows in a wide range of Reynolds numbers (from 500 to 5.25×‎106‎) and angles of attack (from 0 to 20 degrees) around three airfoils of NACA0012, ONERA, and S809 is provided. Also, a comprehensive sensitivity study (including investigating the effects of the CFL number, artificial compressibility coefficient β), artificial dissipation coefficient (ε_4), position of the first row of nodes (y^+), and the power of preconditioning factor (m) has been done to evaluate the accuracy and efficiency of the power-law preconditioning algorithm with the aid of characteristic boundary conditions. After checking the accuracy of the results, the effect of using characteristic non-reflective boundary conditions in the power-law preconditioning method on the convergence rate has been investigated. Using characteristic non-reflective boundary conditions instead of common reflective boundary conditions has not impaired the accuracy of solving the problem, and in some cases, especially in turbulent flows, it has improved the accuracy of the numerical solution. The effect of the combination of non-reflective characteristic boundary conditions and the power-law preconditioning method on the rate of convergence and reducing the number of iterations of the solution has been very dramatic, and in some of the studied problems, it leads to an increase in the speed of convergence up to 70 percent‎‎.‎