Mehrdad T. Manzari

Bio: Mehrdad T. Manzari is an academic researcher from Sharif University of Technology. The author has contributed to research in topics: Finite element method & Discretization. The author has an hindex of 16, co-authored 49 publications receiving 1061 citations. Previous affiliations of Mehrdad T. Manzari include King's College, Aberdeen & University of Aberdeen.

Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives

Abstract: Several schemes for discretization of first and second derivatives are available in Smoothed Particle Hydrodynamics (SPH). Here, four schemes for approximation of the first derivative and three schemes for the second derivative are examined using a theoretical analysis based on Taylor series expansion both for regular and irregular particle distributions. Estimation of terms in the truncation errors shows that only the renormalized (the first-order consistent) scheme has acceptable convergence properties to approximate the first derivative. None of the second derivative schemes has the first-order consistency. Therefore, they converge only when the particle spacing decreases much faster than the smoothing length of the kernel function. In addition, using a modified renormalization tensor, a new SPH scheme is presented for approximating second derivatives that has the property of first-order consistency. To assess the computational performance of the proposed scheme, it is compared with the best available schemes when applied to a 2D heat equation. The numerical results show at least one order of magnitude improvement in accuracy when the new scheme is used. In addition, the new scheme has higher-order convergence rate on regular particle arrangements even for the case of only four particles in the neighborhood of each particle.

A fully explicit three‐step SPH algorithm for simulation of non‐Newtonian fluid flow

Abstract: Purpose – This paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.Design/methodology/approach – The governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same ...

An explicit finite element algorithm for convection heat transfer problems

Abstract: A finite element algorithm is presented for the simulation of steady incompressible fluid flow with heat transfer using triangular meshes. The continuity equation is modified by employing the artificial compressibility concept to provide coupling between the pressure and velocity fields of the fluid. A standard Galerkin finite element method is used for spatial discretization and an explicit multistage Runge‐Kutta scheme is used to march in the time domain. The resulting procedure is stabilized using an artificial dissipation technique. To demonstrate the performance of the proposed algorithm a wide range of test cases is solved including applications with and without heat transfer. Both natural and forced convection applications are studied.

A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows

Abstract: A weakly compressible smoothed particle hydrodynamics (WCSPH) method is used along with a new no-slip boundary condition to simulate movement of rigid bodies in incompressible Newtonian fluid flows. It is shown that the new boundary treatment method helps to efficiently calculate the hydrodynamic interaction forces acting on moving bodies. To compensate the effect of truncated compact support near solid boundaries, the method needs specific consistent renormalized schemes for the first and second-order spatial derivatives. In order to resolve the problem of spurious pressure oscillations in the WCSPH method, a modification to the continuity equation is used which improves the stability of the numerical method. The performance of the proposed method is assessed by solving a number of two-dimensional low-Reynolds fluid flow problems containing circular solid bodies. Wherever possible, the results are compared with the available numerical data.

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

Abstract: In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

Smoothed Particle Hydrodynamics and Its Diverse Applications

Abstract: This review focuses on the applications of smoothed particle hydrodynamics (SPH) to incompressible or nearly incompressible flow. In the past 17 years, the range of applications has increased as researchers have realized the ability of SPH algorithms to handle complex physical problems. These include the disruption of free surfaces when a wave hits a rocky beach, multifluid problems that may involve the motion of rigid and elastic bodies, non-Newtonian fluids, virtual surgery, and chemical precipitation from fluids moving through fractured media. SPH provides a fascinating tool that has some of the properties of molecular dynamics while retaining the attributes of the macroscopic equations of continuum mechanics.

Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future

Abstract: This paper assesses some recent trends in the novel numerical meshless method smoothed particle hydrodynamics, with particular focus on its potential use in modelling free-surface flows. Due to its Lagrangian nature, smoothed particle hydrodynamics (SPH) appears to be effective in solving diverse fluid-dynamic problems with highly nonlinear deformation such as wave breaking and impact, multi-phase mixing processes, jet impact, sloshing, flooding and tsunami inundation, and fluid–structure interactions. The paper considers the key areas of rapid progress and development, including the numerical formulations, SPH operators, remedies to problems within the classical formulations, novel methodologies to improve the stability and robustness of the method, boundary conditions, multi-fluid approaches, particle adaptivity, and hardware acceleration. The key ongoing challenges in SPH that must be addressed by academic research and industrial users are identified and discussed. Finally, a roadmap is propose...

A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution

Abstract: This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.