M. Serdar Celebi

NONLINEAR MODELING OF LIQUID SLOSHING IN A MOVING RECTANGULAR TANK

Abstract A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results.

Analysis of the effects of different pulsatile inlet profiles on the hemodynamical properties of blood flow in patient specific carotid artery with stenosis

In this study the biomechanical characteristics of a realistic carotid artery [3] are studied numerically using different inlet velocity profiles. Several experimental data measured [32] at the common carotid artery are used as inlet boundary conditions. Computation domain is generated using computed tomography (CT) data of a real patient. Three dimensional (3D) transient NS equations are solved, in this actual domain, using the proposed boundary conditions. Effects of different input conditions on the results of simulation are discussed. Main parameters such as velocity profiles, wall shear stress (WSS) and pressure distributions are investigated at the critical parts of the carotid artery such as bifurcation and sinusoidal enlargement regions. Results show that the input boundary conditions and slope/curvature discontinuities in the realistic geometry have strong relationship with the velocity, pressure and WSS distributions as expected. The most important conclusion obtained from our model is the existence of negative relation between velocity at several inner points of the internal carotid artery and velocity at the inlet of the common carotid artery.

Real-time deformation simulation of non-linear viscoelastic soft tissues

Real-time soft-tissue simulation has gained great interest recently as a result of advancements in areas such as surgery planning and surgical simulations. Linear deformation models may not provide the required accuracy in such areas whilst non-linear models do not serve the real-time needs. Therefore, there is a common need for a computationally simplified yet accurate, non-linear, large deformable viscoelastic model of soft tissues to be used in these real-time applications. To date, standard non-linear finite-element methods are incapable of providing the real-time performance needs. Addressing this we propose a new hybrid technique that acts on the reduced order static model acquired through the model reduction technique known as Karhunen—Loéve (KL). The dynamic behavior is then obtained by overlaying pre-calculated displacement responses of surface nodes accounting for the time-dependent viscoelastic properties. The results of deformation simulation of viscoelastic soft tissue are compared with the linear approach.

Nonlinear transient wave–body interactions in steady uniform currents

Abstract Fully nonlinear monochromatic wave three-dimensional body interactions are studied with and without the presence of steady uniform currents. The mixed initial boundary value problem is set-up in a numerical wave tank (NWT) and solved by an indirect desingularized boundary integral equation method (DBIEM). The Laplace equation is solved at each time-step and time-dependent nonlinear free surface boundary conditions are simultaneously integrated by a mixed Eulerian–Lagrangian (MEL) method. A piston-type wave maker is used for generating the incident waves and a steady current is imposed everywhere in the computational domain at t =0 + . A spatially varying sponge layer on the free surface is devised to dissipate the outgoing waves. The resulting influence coefficient matrix is divided into sub-matrices by domain decomposition technique and solved simultaneously by block line Jacobi method (BJM). A specially devised preconditioning matrix is used to accelerate the convergence rate of the matrix equation by obtaining the minimized condition number of the influence coefficient matrix. Computations are performed for the nonlinear diffractions of steep monochromatic waves by a truncated vertical cylinder both without currents and in the presence of uniform coplanar or adverse currents. A φ n -type adaptive beach is developed and its performance compared with some beaches in the literature. Results of NWT simulations are compared with the first-order potential theory (Buchmann et al., Proceedings of the Seventh International Offshore and Polar Engineering Conference, Honolulu, Hawaii, USA, 1997), second-order diffraction theory [Kim and Yue, J. Fluid Mech. 200 (1989) 235–264], modified marker and cell (MAC) method (Park et al., International Journal for Numerical Methods in Fluids 29 (1999) 685–703) and the experimental and second-order potential theory results of Mercier and Niedzwecki [Proceedings of the Seventh International Conference on Behavior of Offshore Structures, vol. 2, TX, USA, 1994, pp. 265–287].

Spectral Analysis of Large Sparse Matrices for Scalable Direct Solvers

It is significant to perform structural analysis of large sparse matrices in order to obtain scalable direct solvers. In this paper, we focus on spectral analysis of large sparse matrices. We believe that the approach for exception handling of challenging matrices via Gerschgorin circles and using tuned parameters is beneficial and practical to stabilize the performance of sparse direct solvers. Nearly defective matrices are among challenging matrices for the performance of solver. Such matrices should be handled separately in order to get rid of potential performance bottleneck. Clustered eigenvalues observed via Gerschgorin circles may be used to detect nearly defective matrix. We observe that the usage of super-nodal storage parameters affects the number of fill-ins and memory usage accordingly.

Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations

An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.

Numerical blood flow simulation with predefined artery movement

In this study, the blood flow in human arteries is modelled. Three dimensional artery geometry is used as the model domain. The geometric model is generated using several parameters of arteries such as radius, length and curvature. After the geometry is determined, blood flow and wall movement models are constructed. For blood flow, Navier-Stokes equations are solved under the assumptions of Newtonian, incompressible flow and constant viscosity. For artery movement, elastic, homogeneous and isotropic material assumptions are implemented. Blood flow and artery movement models are coupled and solved together. The average pressure value acquired from flow model is set as the loading condition of artery movement. The displacement of artery is used to produce new geometry of flow model for the next time step. At the entrance of the artery, Womersley velocity profile is used. This profile is generated using the flow rate data obtained by experimental studies. Thus, the mechanical properties of blood flow such as velocity profiles, wall shear stress and pressure distribution in arteries are investigated. Initial results reveal that that blood flow - artery wall movement coupling model allows to relate the development of vortices, low wall shear stress zones and others to the cardiovascular diseases.

Estimation of quasi-linear viscoelastic material parameters using nonlinear optimization method

The soft tissues are considered as complex materials which are difficult to be modeled due to their nonlinear geometric and material properties, their multilayer structures, large displacements, anisotropic, nonhomogenous and viscoelastic material properties. This study focuses on the error minimization and converge problem in predicting the non-unique material parameters of quasi-linear (QLV) integral form by Fung [5] which is used in modeling viscoelastic material properties of soft tissues. The solution is improved by using refined nonlinear optimization method.

Effects of using depletion interaction theory in variable hematocrit levels of bio-flows

In our study, hematocrit levels and differences in rheological properties of blood, especially in red blood cell (RBC) using depletion interaction theory are investigated. In simulation, we apply depletion interaction theory which is a chemical concept at mesoscale level and unite with bio-fluid mechanics at a macro scale level. In order to differentiate the advantages of this theory, two-phase simulations are performed and RBC aggregation is studied. Wall shear stresses (WSS), phase distributions and volume fractions, with a range of hematocrit levels of RBC are calculated using depletion theory for multi-phase simulation and compared with numerical and experimental data in literature.In our study, hematocrit levels and differences in rheological properties of blood, especially in red blood cell (RBC) using depletion interaction theory are investigated. In simulation, we apply depletion interaction theory which is a chemical concept at mesoscale level and unite with bio-fluid mechanics at a macro scale level. In order to differentiate the advantages of this theory, two-phase simulations are performed and RBC aggregation is studied. Wall shear stresses (WSS), phase distributions and volume fractions, with a range of hematocrit levels of RBC are calculated using depletion theory for multi-phase simulation and compared with numerical and experimental data in literature.

On the improvement of a scalable sparse direct solver for unsymmetrical linear equations

This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server systems taking advantage of both distributed memory and processing units. We conducted extensive numerical experiments with three state-of-the-art direct linear solvers that can work on distributed-memory parallel architectures; namely, MUMPS (MUMPS solver website, http://graal.ens-lyon.fr/MUMPS), WSMP (Technical Report TR RC-21886, IBM, Watson Research Center, Yorktown Heights, 2000), and SUPERLU_DIST (ACM Trans Math Softw 29(2):110–140, 2003). The performance of these solvers was analyzed in detail, using advanced analysis tools such as Tuning and Analysis Utilities (TAU) and Performance Application Programming Interface (PAPI). The performance is evaluated with respect to robustness, speed, scalability, and efficiency in CPU and memory usage. We have determined application level issues that we believe they can improve the performance of a distributed-shared memory hybrid variant of this solver, which is proposed as an alternative solver [SuperLU_MCDT (Many-Core Distributed)] in this paper. The new solver utilizing the MPI/OpenMP hybrid programming is specifically tuned to handle large unsymmetrical systems arising in reservoir simulations so that higher performance and better scalability can be achieved for a large distributed computing system with many nodes of multicore processors. Two main tasks are accomplished during this study: (i) comparisons of public domain solver algorithms; existing state-of-the-art direct sparse linear system solvers are investigated and their performance and weaknesses based on test cases are analyzed, (ii) improvement of direct sparse solver algorithm (SuperLU_MCDT) for many-core distributed systems is achieved. We provided results of numerical tests that were run on up to 16,384 cores, and used many sets of test matrices for reservoir simulations with unstructured meshes. The numerical results showed that SuperLU_MCDT can outperform SuperLU_DIST 3.3 in terms of both speed and robustness.