Papers by Fereidoun Sabetghadam
Simulation of solid body motion in a newtonian fluid using a vorticity-based pseudo-spectral immersed boundary method augmented by the radial basis functions
International Journal of Modern Physics C, 2014
A vorticity based approach to handle the fluid-structure interaction problems
Fluid Dynamics Research, 2016
Storage Schemes Effect on the CPU-Time of the Krylov Subspace Methods in Solving the Linear Systems Arising from CFD
Choosing an appropriate storage scheme in solution of the sparse systems vigorously affects the c... more Choosing an appropriate storage scheme in solution of the sparse systems vigorously affects the computational time of the Krylov solvers. In the present study some conventional storage methods, that is, the Coordinate, Compressed Sparse Row (CSR), Modified Sparse Row (MSR), Diagonal and Ellpack-Itpack formats are assessed and last four schemes are compared. The Conjugate Gradient (CG) method and its preconditioned version (ILU(0)-CG) are utilized to solve an elliptic partial differential equation which is discretized using a second order central difference scheme on various computational grids. A comparison based on the CPU-times, corresponding to each storage format is accomplished. The results show that the Diagonal format has the most efficiency among the considered formats. 1. Introduction Discretizing the partial differential equations (PDEs) commonly leads to large sparse matrices. A sparse matrix has many zero elements and some efficient schemes which exploit the structure of...
Journal of Mechanics, 2015
A new simulation method for solving fluid-structure two-way coupling problems has been developed.... more A new simulation method for solving fluid-structure two-way coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A new definition of velocity-vorticity formulation aids us to introduce an immersed boundary method that does not require a force term to impose the no-slip condition on the solid boundaries. The proposed method is easy to implement and apply for two-way fluid-structure interaction problems. The dynamics of a falling and rising circular cylinder in a quiescent fluid as well as the motion of a circular cylinder in a lid-driven cavity are considered to evaluate the capabilities of the presented method.
Journal of Mechanics, 2014
An immersed boundary method is proposed for the simulation of the interaction of an incompressibl... more An immersed boundary method is proposed for the simulation of the interaction of an incompressible flow with rigid bodies. The method is based on a new interpretation of velocity-vorticity formulation and no longer includes the force term which is an essential issue of common immersed boundary methods. The system is considered in an Eulerian frame and retrieving the vorticity in this formulation enforces continuity at the fluid-solid interface and rigid motion of the solid. The method focuses on the mutual kinematic relations between the velocity and vorticity fields and with retrieving the vorticity field and recalculating the velocities yields the solenoidal velocity field. The method is applied to the two dimensional problems and the results show that the solenoidality is satisfied acceptably. The comparisons with 2D test cases are provided to illustrate the capabilities of the proposed method.
Applied Mathematics and Computation, 2012
a Regularization Helmholtz filtering Eigenvalue analysis a b s t r a c t In order to improve the ... more a Regularization Helmholtz filtering Eigenvalue analysis a b s t r a c t In order to improve the dynamics and stability of the POD-Galerkin models of strongly-stiff systems, an a-like regularization is suggested and assessed in the present article. In this method, the POD eigenmodes of the non-linear terms are replaced by their Helmholtz filtered counterparts, while the other terms are remained unchanged. As an example, the method is applied to the POD-Galerkin models of the one-dimensional Kuramoto-Sivashinsky (KS) equation in a full chaotic regime; and the fidelity of the original and regularized models to the direct numerical simulations (DNS) are investigated. Moreover, the effects of regularization on the dynamics of various terms, and whole of the systems, are analyzed via eigenvalue analysis of each term separately, and the total dynamical system as a whole. The numerical experiments show definite effectiveness of the method and excellent improvements in the predicted dynamics and stability, by minimum number of free parameters.
Mean Model Analysis of the Coherent Structures in a Two-dimensional Vortex Merger
Progress in Turbulence Ii, 2007
A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method
Http Dx Doi Org 10 1080 10407790 2013 784136, Sep 17, 2013
ABSTRACT A least-squares algorithm for handling complex boundaries with the lattice Boltzmann met... more ABSTRACT A least-squares algorithm for handling complex boundaries with the lattice Boltzmann method is proposed. The method is an extension to an immersed boundary implementation of the solver. We impose additional rules that are designed to conserve the mass flux through cut-cell control volumes and also to satisfy the continuity condition on the numerical boundary points. Then, we use the least-squares method to find the best achievable solution of the overdetermined system. Further, computational cost assessments are considered. The qualitative and quantitative results show that the velocity values obtained from simulation of a flow with curved and moving boundaries, i.e., the Taylor-Couette flow, are closer to the exact solution than the values found from the traditional approach. Finally, we present some statistical analysis to show that the velocities are obtained confidently.
The present paper is devoted to implementation of the immersed boundary technique into the Fourie... more The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to many other similar methods, there is not an explicit external forcing function in the present formulation. The desired immersed boundary conditions are approximated on some regular grid points, using different orders (up to second-order) polynomial extrapolations. At the beginning of each timestep, the solenoidal velocities (also satisfying the desired immersed boundary conditions), are obtained and fed into a conventional pseudo-spectral solver, together with a modified vorticity. The zero-mean pseudo-spectral solution is employed, and therefore, the method is applicable to the confined flows with zero mean velocity and vorticity, and without mean vorticity dynamics. In comparison to the classical Fourier pseudo-spectral solution, the method needs O(4(1 + log N )N ) more operations for boundary condition settings. Therefore, the computational cost of the method, as a whole, is scaled by . The classical explicit fourth-order Runge-Kutta method is used for time integration, and the boundary conditions are set at the beginning of each sub-step, in order to increasing the time accuracy. The method is applied to some fixed and moving boundary problems, with different orders of boundary conditions; and in this way, the accuracy and performance of the method are investigated and compared with the classical Fourier pseudo-spectral solutions.
Analysis of the Applicability of the Lattice Boltzmann Method in Targeting a Chaotic Flame Front Model
Http Dx Doi Org 10 1080 10407782 2014 937264, Dec 10, 2014
ABSTRACT In this paper, we present utilization of the lattice Boltzmann method (LBM) to analyze s... more ABSTRACT In this paper, we present utilization of the lattice Boltzmann method (LBM) to analyze spatiotemporal chaotic fields. To this end, the one-dimensional Kuramoto–Sivashinsky equation, which is a proper model for unstable flame front flutter, is rewritten in terms of lattice Boltzmann equation components and is then solved. After accuracy checks, we alter the computational domain size and also the control parameter of the problem, which is representative of the kinematic viscosity in real flows, to capture the symmetry-breaking phenomenon. In the next step, since the method is in fact a one-dimensional explicit mapping for the probability density functions, we adopt the targeting algorithm of chaotic fields using LBM. The results show that the method can be applied to chaotic fields with confidence.
The present paper suggests a method for obtaining incompressible solenoidal velocity vectors that... more The present paper suggests a method for obtaining incompressible solenoidal velocity vectors that satisfy approximately the desired immersed velocity boundary conditions. The method employs merely the mutual kinematic relations between the velocity and vorticity fields (i.e, the curl and Laplacian operators). An initial non-solenoidal velocity field is extended to a regular domain via a zero-velocity margin, where an extended vorticity is found. Re-calculation of the velocities (subjected to appropriate boundary conditions), yields the desired solenoidal velocity vector. The method is applied to the two- and three-dimensional problems for the homogeneous Dirichlet, as well as periodic boundary conditions. The results show that the solenoidality is satisfied up to the machine accuracy for the periodic boundary conditions (employing the Fourier--spectral solution method), while an improvement in the solenoidality is achievable for the homogenous boundary conditions.
Analysis of the Applicability of the Lattice Boltzmann Method in Targeting a Chaotic Flame Front Model
Numerical Heat Transfer, Part A: Applications, 2014
ABSTRACT In this paper, we present utilization of the lattice Boltzmann method (LBM) to analyze s... more ABSTRACT In this paper, we present utilization of the lattice Boltzmann method (LBM) to analyze spatiotemporal chaotic fields. To this end, the one-dimensional Kuramoto–Sivashinsky equation, which is a proper model for unstable flame front flutter, is rewritten in terms of lattice Boltzmann equation components and is then solved. After accuracy checks, we alter the computational domain size and also the control parameter of the problem, which is representative of the kinematic viscosity in real flows, to capture the symmetry-breaking phenomenon. In the next step, since the method is in fact a one-dimensional explicit mapping for the probability density functions, we adopt the targeting algorithm of chaotic fields using LBM. The results show that the method can be applied to chaotic fields with confidence.
Springer Proceedings in Physics, 2007
Mean Model Analysis of the Coherent Structures in a Two-dimensional Vortex Merger
The present paper is devoted to implementation of the immersed boundary technique into the Fourie... more The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to many other similar methods, there is not an explicit external forcing function in
A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method
Numerical Heat Transfer, Part B: Fundamentals, 2013
ABSTRACT A least-squares algorithm for handling complex boundaries with the lattice Boltzmann met... more ABSTRACT A least-squares algorithm for handling complex boundaries with the lattice Boltzmann method is proposed. The method is an extension to an immersed boundary implementation of the solver. We impose additional rules that are designed to conserve the mass flux through cut-cell control volumes and also to satisfy the continuity condition on the numerical boundary points. Then, we use the least-squares method to find the best achievable solution of the overdetermined system. Further, computational cost assessments are considered. The qualitative and quantitative results show that the velocity values obtained from simulation of a flow with curved and moving boundaries, i.e., the Taylor-Couette flow, are closer to the exact solution than the values found from the traditional approach. Finally, we present some statistical analysis to show that the velocities are obtained confidently.
Journal of Computational Physics, 2009
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Papers by Fereidoun Sabetghadam