Sharif Digital Repository

In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the... 

A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth-order compact FD scheme, and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also... 

A high-order compact finite-difference scheme is applied and assessed for the numerical simulation of structural dynamics. The two-dimensional elastic stress-strain equations are considered in the generalized curvilinear coordinates and the spatial derivatives in the resulting equations are discretized by a fourth-order compact finite-difference scheme. For the time integration, an implicit second-order dual time-stepping method is utilized in which a fourth-order Runge-Kutta scheme is used to integrate in the pseudo-time level. The accuracy and robustness of the solution procedure proposed are investigated through simulating different two-dimensional benchmark test cases in structural... 

A high-order compact finite-difference total Lagrangian method (CFDTLM) is developed and applied to nonlinear structural dynamic analysis. The two-dimensional simulation of thermo-elastodynamics is numerically performed in generalized curvilinear coordinates by taking into account the geometric and material nonlinearities. The spatial discretization is carried out by a fourth-order compact finite-difference scheme and an implicit second-order accurate dual time-stepping method is applied for the time integration. The accuracy and capability of the proposed solution methodology for the nonlinear structural analysis is investigated through simulating different static and dynamic benchmark... 

In this work, a preconditioned high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (WENO-LBM) is applied to deal with the incompressible turbulent flows. Two different turbulence models namely, the Spalart–Allmaras (SA) and k−ωSST models are used and applied in the solution method for this aim. The spatial derivatives of the two-dimensional (2D) preconditioned LB equation in the generalized curvilinear coordinates are discretized by using the fifth-order WENO finite-difference scheme and an implicit–explicit Runge–Kutta scheme is adopted for the time discretization. For the convective and diffusive terms of the turbulence transport equations, the... 

In this work, the capability and performance of the vorticity confinement (VC) implemented in a high-order accurate flow solver in predicting two-dimensional (2D) compressible mixing layer flows on coarse grids are investigated. Here, the system of governing equations with incorporation of the VC in the formulation is numerically solved by the fourth-order compact finite difference scheme. To stabilize the numerical solution, a low-pass high-order filter is applied, and the nonreflective boundary conditions are used at the farfield and outflow boundaries to minimize the reflections. At first, the numerical results without applying the VC are validated by available direct numerical... 

In the present study, the preconditioned incompressible Navier-Stokes equations with the artificial compressibility 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 in a wide range of Reynolds numbers. A fourth-order compact finite-difference scheme is utilized to accurately discretize the spatial derivative terms of the governing equations, and the time integration is carried out based on the dual time-stepping method. The capability of the proposed solution methodology for the computations of the steady and unsteady incompressible... 

In the present study, a high-order compact finite-difference lattice Boltzmann method is applied for accurately computing 3-D incompressible flows in the generalized curvilinear coordinates to handle practical and realistic geometries with curved boundaries and nonuniform grids. The incompressible form of the 3-D nineteen discrete velocity lattice Boltzmann method is transformed into the generalized curvilinear coordinates. Herein, a fourth-order compact finite-difference scheme and a fourth-order Runge-Kutta scheme are used for the discretization of the spatial derivatives and the temporal term, respectively, in the resulting 3-D nineteen discrete velocity lattice Boltzmann equation to... 

In the present study, a high-order compact finite-difference lattice Boltzmann method is applied for accurately computing 3-D incompressible flows in the generalized curvilinear coordinates to handle practical and realistic geometries with curved boundaries and nonuniform grids. The incompressible form of the 3-D nineteen discrete velocity lattice Boltzmann method is transformed into the generalized curvilinear coordinates. Herein, a fourth-order compact finite-difference scheme and a fourth-order Runge-Kutta scheme are used for the discretization of the spatial derivatives and the temporal term, respectively, in the resulting 3-D nineteen discrete velocity lattice Boltzmann equation to... 

The objective of this work is to numerically study the fluid flow and acoustic field of a supersonic impinging jet by applying the vorticity confinement (VC) method. For this aim, the three-dimensional compressible Navier-Stokes equations with the incorporation of the VC method are considered and the resulting system of equations is solved by using the sixth-order compact finite-difference scheme. To eliminate the numerical instability, a low-pass high-order filter is used. The nonreflective boundary conditions are applied for all the free boundaries and the radiated sound field is obtained by the Kirchhoff surface integration. Comparisons of the present results with the experimental data... 

The objective of this work is to numerically study the fluid flow and acoustic field of a supersonic impinging jet by applying the vorticity confinement (VC) method. For this aim, the three-dimensional compressible Navier-Stokes equations with the incorporation of the VC method are considered and the resulting system of equations is solved by using the sixth-order compact finite-difference scheme. To eliminate the numerical instability, a low-pass high-order filter is used. The nonreflective boundary conditions are applied for all the free boundaries and the radiated sound field is obtained by the Kirchhoff surface integration. Comparisons of the present results with the experimental data... 

In this study, the nonlinear partial differential equations governing two phase flow through porous media are solved using two different methods, namely, finite difference and finite element. The capillary pressure term is considered in the mathematical model. The numerical results on a 2-D test case are then compared with the experimental drainage process and water flooding performed on a glass type micromodel. Based on the obtained results, finite difference technique needs less computational time for solving governing equations of two phase flow, but findings of this method show less agreement with the experimental data. The finite element scheme was found to be more adequate and its... 

The main goal of this study is to assess the application of high-order compact finite-difference schemes for the solution of the Euler equations in conjunction with the compressible vorticity confinement method on both uniform Cartesian and curvilinear grids. Here, the spatial discretization of the governing equations is performed by the fourth-order compact finite-difference scheme and the temporal term is discretized by the fourth-order Runge-Kutta method. To stabilize the numerical solution, appropriate dissipation terms are applied and a detail assessment is performed to study the effects of the values of confinement and dissipation coefficients on the solution to reasonably preserve the... 

This paper has developed an axisymmetric laminar and turbulent two-phase flow solver to simulate pressure-swirl atomizers. Equations include the explicit algebraic Reynolds stress model, the Reynolds-averaged Navier-Stokes, and the level set equation. Applying a high-order compact upwind finite difference scheme with the level set equation being culminated to capture the interface between air-liquid two-phase flow and decreasing the mass conservation error in the level set equation. The results show that some recirculation zones are observed close to the wall in the swirl chamber and to the axis. This model can predict converting the Rankin vortex in the swirl chamber to the forced vortex in... 

This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind,... 

A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is extended and applied to accurately simulate two-phase liquid-vapor flows with high density ratios. Herein, the He-Shan-Doolen-type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equations are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A high-order spectral-type low-pass compact nonlinear filter is used to regularize the numerical solution and remove spurious waves generated by flow nonlinearities in smooth regions... 

In this study, the fundamental problem of unsteady blood flow in a tube with multi-stenosis is studied. An appropriate shape of the time-dependent multi-stenosis which is overlapping in the realm of formation of arterial narrowing is constructed mathematically. Blood is considered as a viscoelastic fluid characterized by the Oldroyd-B model. For the numerical solution of the problem, which is described by a coupled, non-linear system of partial differential equations (PDEs), with appropriate boundary conditions, the finite difference scheme is adopted. The solution is obtained by the development of an efficient numerical methodology based on the predictor-corrector method. The effects of... 

Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in... 

This study reports on the simulation of temperature distribution of human tooth under a laser beam based on non-Fourier models. The temperature in the tooth depth that directly results from the conduction heat transfer process is caused by the lengthy thermal relaxation time in the tooth layers. A detailed tooth composed of enamel, dentin, and pulp with unstructured shape, uneven boundaries, and realistic thicknesses was considered. A finite difference scheme was separately adopted to solve time-dependent equations in solid layers and soft tissue of the tooth. In this study, a dual-phase-lag non-Fourier heat conduction model was applied to evaluate temperature distribution induced by laser...