Sharif Digital Repository

The objective of this study is to develop and apply an arbitrary Lagrangian-Eulerian unstructured finite-volume lattice-Boltzmann method (ALE-FVLBM) for solving two-dimensional compressible flows around moving bodies. The two-dimensional compressible form of the LB equation, along with the Batangar-Gross-Crook (BGK) approximation for modeling the collision operatore, and the D2Q65 Watari model for modeling the equilibrium distribution function, are considered here. The resulting LB equation is formulated in the ALE framework on an unstructured body-fitted mesh to correctly model the body shape and properly incorporate the mesh movement due to the body motion. The spatial discretization of... 

In this study, a gas kinetic model is presented and applied to investigate the compressible rarefied gas flows with nonequilibrium chemical reactions effects. The formulation of the Boltzmann equation is extended to incorporate these chemical reactions, and the resulting equations are numerically solved using the fifth-order WENO finite difference method to achieve high accuracy. The present research focuses on solving one-dimensional flows. After developing the WENO-based Boltzmann solver, its validation is performed through numerical simulations of different one-dimensional shock tube problems under different conditions. The results show good agreement with existing results, confirming the... 

The main objective of this study is to evaluate the accuracy and performance of the vorticity confinement (VC) method implemented in a second-order finite volume flow solver for solving two-dimensional compressible mixing layer flows. The spatial discretization of the system of governing equations is performed by a second-order central difference finite volume method and a fourth-order Runge-Kutta method is used for the time integration. To have a stable solution, the second- and fourth-order numerical dissipation terms are applied. At first, two problems, namely, the advection of an isentropic vortex and the shock-vortex interaction are numerically solved and the effects of the confinement... 

The precise and efficient determination of aerodynamic coefficients for flying bodies is crucial for analyzing their flight trajectory and stability behavior. Given the high cost of experimental tests, the use of computational fluid dynamics (CFD) methods for determining the aerodynamic characteristics of flying bodies has become feasible in recent years due to the availability of powerful and fast computers and the development of effective numerical algorithms. In this research, the calculation of the aerodynamic coefficients for arbitrary three-dimensional flying bodies is carried out using an efficient method. For this purpose, the unsteady flow simulation over the flying body is... 

In the present study, the compressible form of the lattice Boltzmann (LB) equation with the Bhatnagar-Gross-Krook (BGK) model is considered and reformulated to account for real gas effects by incorporating the relations of the equilibrium air model in the formulation. Here, two compressible LB models, namely, the Watari and Kataoka-Tsutahara models are applied to estimate the lattice velocity and the equilibrium distribution function. To properly model the geometries with the curve boundaries, the LB formulation is transformed to the generalized curvilinear coordinates. The spatial discretization of the resulting LB formulation is performed using the high-order weighted essentially... 

The production of agricultural products is one of the most important human economic activities. The issue of mechanized and optimal use of pesticides is vital for human health and the environment, and the use of helicopters makes this possible. Although spray-based systems in helicopters are one of the most effective ways to produce agricultural products, it is still unclear how droplet movement in aerial spraying is affected by the complex downwash flow created by rotors. Modeling agricultural air spray to identify the spray trend of droplets in the air stream, downwash flows, and consequent vortices has attracted more attention as a result of the development of computational fluid... 

In this study, the Shokov-BGK model of the Boltzmann equation is reformulated and generalized to consider the real gas effects. At first, the formulation is performed to consider an arbitrary specific heats ratio and the correct Prandtl number for polyatomic gases. Here, the resulting equations of the present formulation are numerically solved by applying the high-order finite-difference weighted essentially non-oscillatory (WENO) scheme. The present solution method is tested by computing the one-dimension Reiman problem with different specific heats ratios for a wide range of the Knudsen numbers. The results are compared with the available gas-kinetic results which show good agreement. It... 

In this study, a high-order finite-difference lattice Boltzmann method (FDLBM) is used to simulate the two-dimensional incompressible flows. Here, the incompressible form of the lattice Boltzmann (LB) equation in the two-dimensional generalized curvilinear coordinates is considered and the resulting equation is discretized based on both the third- and fifth-order upwind finite-difference schemes. The time integration of the present flow solver is performed by the fourth-order Runge-Kutta method. Several incompressible laminar flow problems are simulated to examine the accuracy and performance of the developed high-order FDLBM solver. The present results are compared with the existing... 

In the present study, a high-order finite-difference lattice Boltzmann solver is applied for simulating steady and unsteady three-dimensional incompressible flows. To achieve an accurate and robust flow solver, the incompressible form of the lattice Boltzmann equation in the three-dimensional generalized curvilinear coordinates is discretized spatially based on the fifth-order weighted essentially non-oscillatory (WENO) finite-difference scheme. To ensure the stability and temporal accuracy of the flow solver, the fourth-order Runge-Kutta method is used for the time integration. To examine the accuracy and performance of the flow solver, different three-dimensional incompressible flow... 

In the present study, the numerical simulation of 2D inviscid compressible cavitation flow is performed by using the compact finite-difference method. The problem formulation is based on the multiphase compressible Euler equations with the assumption of the homogeneous equilibrium model and the system of baseline differential equations is comprised of the continuity, momentum and energy equations for the vapor-liquid mixture. To complete the system of governing equations, the ideal gas relation is used for the vapor phase and the Tait relation is applied for the liquid phase, and therefore, the compressibility effects are considered for both the vapor and liquid phases. To analyze the flow... 

In this work, a high-order accurate gas kinetic scheme based on the compact finite-difference Boltzmann method (CFDBM) is developed and applied for simulating the compressible rarefied gas flows. Here, the Shakhov model of the Boltzmann equation is considered and the spatial derivative term in the resulting equation is discretized by using the fourth-order compact finite-difference method and the time integration is performed by using the third-order TVD Runge-Kutta method. A filtering procedure with three discontinuity-detecting sensors is applied and examined for the stabilization of the solution method especially for the problems involving the discontinuity regions such as the shock. The... 

In this research, the numerical simulation of the natural convection is performed by using the smoothed particle hydrodynamics based on the artificial compressibility method. For this aim, the formulation of the artificial compressibility method in the Eulerian reference frame for the mass and momentum equations is written in the Lagragian reference frame and the Lagrangin form of the energy equation is also considered to compute the thermal effects. The benefit of the artificial compressibility-based incompressible SPH (ACISPH) method over the weakly compressible SPH (WCSPH) method for computing the natural convection is that there is no need in the formulation considered here to use any... 

In this research, the spectral difference lattice Boltzmann method (SDLBM) is developed and applied for an accurate simulation of two-dimensional (2D) inviscid and viscous compressible flows on the structured and unstructured meshes. The compressible form of the discrete Boltzmann-BGK equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid. Here, the 2D compressible Lattice Boltzmann (LB) model proposed by Watari is used. The spectral difference (SD) method is implemented for the solution of the LB equation in which the particle distribution functions are stored at the solution points while the fluxes are calculated... 

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is applied and assessed for the simulation of the non-cavitating/cavitating flows. At first, the basic formulation of the NDGM is explained and the properties of the solution method of the NDGM are studied by solving the one-dimensional wave equation. Then, the one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the NDGM and the third-order TVD Runge–Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity... 

In the present study, an incompressible smoothed particle hydrodynamics based on the artificial compressibility method is applied for simulating the incompressible turbulent flows. The Reynolds-averaged incompressible Navier–Stokes equations using the artificial compressibility method in the Eulerian reference frame are written in the Lagrangian reference frame to provide an appropriate incompressible SPH algorithm for the turbulent flow computations. Here, the k-L_m turbulence model, which is a simplified k-ϵ turbulence model, is used and formulated in the Lagrangian reference frame. The SPH formulation implemented here is based on an implicit dual-time stepping scheme to be capable of... 

In the present study, the preconditioned incompressible Navier‐Stokes equations with the artificial compressibility (AC) method formulated in the generalized curvilinear coordinates are numerically solved by using a high‐order compact finite‐difference scheme for accurately and efficiently computing the incompressible flows. A fourth‐order compact finite‐difference scheme is utilized to discretize the spatial derivative terms of the resulting system of equations and the time integration is carried out based on the dual time‐stepping method. The capability of the proposed solution methodology for computing the steady and unsteady incompressible viscous flows in a wide range of Reynolds... 

In the present study, the shock-disturbances interaction in hypersonic inviscid flows considering real gas effects is numerically studied by using a high-order WENO scheme. To account for real gas effects, the equilibrium air model is utilized. The strong conservative form of the two-dimensional unsteady Euler equations in the generalized curvilinear coordinates is considered as the governing equations and a shock-capturing technique is applied. The resulting system of equations is discretized by using the fifth-order WENO finite-difference scheme in space and the explicit third-order TVD Runge-Kutta scheme in time to provide a high-order accurate flow solver. The WENO scheme is a stable scheme... 

The goal of this thesis is the development and application of the finite volume method (FVM) with a same solution procedure in the fluid and structure domains for the simulation of fluid-structure interaction (FSI) problems in the compressible fluid flow. The unsteady Euler equations written in the arbitrary Lagrangian–Eulerian (ALE) form are considered as the governing equations of the compressible fluid flow and the moderate/large nonlinear deformation of the elastic structure is considered to be governed by the Cauchy equations in the Lagrangian/total Lagrangian forms. Therefore, the nonlinear phenomena in the unsteady compressible fluid flow and the large deformation of the elastic... 

In the present study, the numerical simulation of the panel flutter in compressible inviscid flow is performed by the compact finite difference method. For this purpose, the 2D compressible Euler equations written in the arbitrary Lagrange-Eulerian form are considered and the resulting system of equations in the generalized curvilinear coordinates is solved by the fourth-order compact finite-difference method. An appropriate nonlinear filter is applied for the shock capturing and for the solution to be stable. The governing equation for the panel is also numerically solved by using the fourth-order compact finite difference method. The time integration in the flow domain is made by the...