Sharif Digital Repository

Interaction of freestream disturbances with high-speed inviscid flow over a blunt nose is simulated utilizing a shock-fitted spectral collocation method. The unsteady flow computations are made through solving the 2D Euler equations by virtue of such a dissipation-free numerical algorithm for precise unsteady flow simulations. A shock-fitting technique is employed to accurately compute the unsteady shock motions and its interaction with monochromatic freestream disturbances of different conditions. A symmetry condition is proposed to accurately model the both steady and unsteady characters of the symmetry boundary, which allows the use of halved geometries and avoids the extra computational... 

An improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet-cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow-field by a power-law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell-centered Jameson's finite volume algorithm. The stabilization is achieved via the second-and fourth-order artificial dissipation... 

A new shock-detecting sensor for properly switching between a second-order and a higher-order filter is developed and assessed. The sensor is designed based on an order analysis. The nonlinear filter with the proposed sensor ensures damping of the high-frequency waves in smooth regions and at the same time removes the Gibbs oscillations around the discontinuities when using high-order compact finite difference schemes. In addition, a suitable scaling is proposed to have dissipation proportional to the shock strength and also to minimize the effects of the second-order filter on the very small scales. Several numerical experiments are carried out and the accuracy of the nonlinear filter with... 

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... 

A new method of spatial filtering in high-order finite volume methods is presented and assessed. The base of this method is to filter face-averaged variables (fluxes) and then the recovery of cell-averaged ones. Two kinds of filtering method are proposed. The first kind is highly dissipative and appropriate for the numerical regions that need high dissipation, e.g. sponge zones. The second kind, on the other hand, is a precise method and hence is suitable for applying the high-order finite difference filters to the finite volume methods. Applying high-order finite difference filters directly to the high-order finite volume methods without using the proposed method causes stability problems... 

The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary... 

In the present study, a truly incompressible smoothed particle hydrodynamics based on the artificial compressibility method for simulating steady and unsteady incompressible flows is proposed and assessed. The incompressible Navier–Stokes equations in the primitive variables formulation using the artificial compressibility method proposed by Chorin in the Eulerian reference frame are written in a Lagrangian reference frame to provide an appropriate incompressible SPH algorithm. The proposed SPH formulation implemented here is based on an implicit dual-time stepping scheme to be capable of time-accurate analysis of unsteady flows. The advantage of the Artificial Compressibility-based... 

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... 

The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary... 

In this study, the numerical simulation of the fluid flow and acoustic field of a supersonic jet is performed by using high-order discretization and the vorticity confinement (VC) method on coarse grids. The three-dimensional Navier-Stokes equations are considered in the generalized curvilinear coordinate system and the high-order compact finite-difference scheme is applied for the space discretization, and the time integration is performed by the fourth-order Runge-Kutta scheme. A low-pass high-order filter is applied to stabilize the numerical solution. The non-reflecting boundary conditions are adopted for all the free boundaries, and the Kirchhoff surface integration is utilized 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... 

In this work, the spectral difference lattice Boltzmann method (SDLBM) is extended and applied for accurately computing two-dimensional viscous compressible flows on structured meshes. Here, the compressible form of the discrete Boltzmann-BGK equation with the Watari model is considered and the numerical solution of the resulting LB equation is obtained by using the spectral difference method. The main benefit of the use of the LB method in simulating compressible flows is that a same formulation can be applied to compute the inviscid and viscous portions of the flowfield. Note that the LB formulation for simulating the viscous flows is the same as that used for the inviscid ones, however,... 

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, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping... 

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several... 

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flowsolver. The spatial derivative terms of the systemof equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried... 

In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The...