Cetin Kiris

Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The equations are solved with a line-relaxation scheme that allows the use of very large pseudotime steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. The steady-state solution of flow through a square duct with a 90-deg bend is computed, and the results are compared with experimental data. Good agreement is observed. Computations of unsteady flow over a circular cylinder are presented and compared to other experimental and computational results. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented. 28 refs.

Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

Computational Approach for Probing the Flow Through Artificial Heart Devices

Computational fluid dynamics (CFD) has become an indispensable part of aerospace research and design. The solution procedure for incompressible Navier-Stokes equations can be used for biofluid mechanics research. The computational approach provides detailed knowledge of the flowfield complementary to that obtained by experimental measurements. This paper illustrates the extension of CFD techniques to artificial heart flow simulation. Unsteady incompressible Navier-Stokes equations written in three-dimensional generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudocompressibility approach. It uses an implicit upwind-differencing scheme together with the Gauss-Seidel line-relaxation method. The efficiency and robustness of the time-accurate formulation of the numerical algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated by experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapped grid embedding scheme are employed, respectively. Steady-state solutions for the flow through a tilting-disk heart valve are compared with experimental measurements. Good agreement is obtained. Aided by experimental data, the flow through an entire Penn State artificial heart model is computed.

Numerical solution of incompressible Navier-Stokes equations using a fractional-step approach

Abstract A fractional step method for the solution of steady and unsteady incompressible Navier–Stokes equations is outlined. The method is based on a finite-volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (third and fifth) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when fifth-order upwind differencing and a modified production term in the Baldwin–Barth one-equation turbulence model are used with adequate grid resolution.

Numerical Simulation of Local Blood Flow in the Carotid and Cerebral Arteries Under Altered Gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.

An Application-Based Performance Characterization of the Columbia Supercluster

Columbia is a 10,240-processor supercluster consisting of 20 Altix nodes with 512 processors each, and currently ranked as one of the fastest computers in the world. In this paper, we present the performance characteristics of Columbia obtained on up to four computing nodes interconnected via the InfiniBand and/or NUMAlink4 communication fabrics. We evaluate floatingpoint performance, memory bandwidth, message passing communication speeds, and compilers using a subset of the HPC Challenge benchmarks, and some of the NAS Parallel Benchmarks including the multi-zone versions. We present detailed performance results for three scientific applications of interest to NASA, one from molecular dynamics, and two from computational fluid dynamics. Our results show that both the NUMAlink4 and In- finiBand interconnects hold promise for multi-node application scaling to at least 2048 processors.

Computation of viscous incompressible flows

1.- Introduction: Flow Physics Computational Approach What is Covered in The Monograph.- 2.- Methods for Solving Viscous Incompressible Flow Problems: Overview Mathematical Model Formulation for General Geometry Overview of Solution Approaches.- 3.- Pressure Projection Method in Generalized Coordinates: Overview Formulation in Integral Form Discretization Solution Procedure Validation of the Solution Procedure.- 4.- Artificial Compressibility Method: Formulation and Its Physical Characteristics Steady-State Formulation Steady-state Algorithm Time-Accurate Procedure Time-Accurate Algorithm Using Upwind Differencing Validation of Solution Procedure Unified Formulation.- 5.- Flow Solvers and Validation: Scope of Validation Selection of Codes for Engineering Applications Steady Internal Flow: Curved Duct with Square Cross-Section Time-Dependent Flow External and Juncture Flow.- 6.- Simulation of Liquid-Propellant Rocket Engine Sub-System: Historical Background Flow Analysis in the Space Shuttle Main Engine (SSME) Flow Analysis Task and Computational Model for the SSME Powerhead Turbulence Modeling Issues Analysis of the Original Three-Circular-Duct HGM Configuration Development of the New Two Elliptic-Duct HGM Configuration.- 7.- Turbo-pump: Historical Background Turbo-pump in Liquid-Propellant Rocket Engine Mathematical Formulation Validation of Simulation Procedures Using an Inducer Application to Impeller Simulation High-Fidelity Unsteady Flow Application to SSME Flowliners.- 8.- Hemodynamics: Introduction Model Equations for Blood Flow Simulation Validation of Simulation Procedure Blood Circulation in Human Brain Simulation of Blood Flow in Mechanical Devices.- References.- Index.

Best Practices for CFD Simulations of Launch Vehicle Ascent with Plumes - OVERFLOW Perspective

A simulation protocol has been developed for modeling rocket plumes of heavy lift launch vehicles (HLLV) during ascent. The procedure uses a series of sensitivity studies applied to the Saturn V launch vehicle to establish accurate plume physics modeling of HLLV main engines. These analyses include a comparison of calorically and thermally perfect gas models, a grid dependence study, a sensitivity analysis of nozzle exit boundary conditions for both single and multi-species gas assumptions, and a thorough turbulence model sensitivity study. The results of the analyses are assessed by comparing the predicted plume induced flow separation (PIFS) distance, an important quantity for thermal protection system design. This quantity is also used to validate the results with existing flight data. The viscous Computational Fluid Dynamics (CFD) code OVERFLOW, a Reynolds Averaged Navier-Stokes flow solver for structured overset grids is utilized. This work is a continuation of the CFD best practices for Ares V aero-database simulation, with the additional complexity of plume physics modeling.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part I: Riemann Problems

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid multicomponent and multiphase flows at all speeds is described. The system is shown to be hyperbolic in time and remains well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. It is well known that the application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces will generate nonphysical pressure and velocity oscillations across the component interface. These oscillations may lead to stability problems when the interface separates fluids with large density ratio, such as water and air. The effect of which may lead to the requirement of small physical time steps and slow subiteration convergence for implicit time marching numerical methods. At low speeds the use of nonconservative methods may be considered. In this paper a characteristic-based preconditioned nonconservative method is described. This method preserves pressure and velocity equilibrium across fluid interfaces, obtains density ratio independent stability and convergence, and remains well conditioned in the incompressible limit of the equations. To extend the method to transonic and supersonic flows containing shocks, a hybrid formulation is described, which combines a conservative preconditioned Roe method with the nonconservative preconditioned characteristic-based method. The hybrid method retains the pressure and velocity equilibrium at component interfaces and converges to the physically correct weak solution. To demonstrate the effectiveness of the nonconservative and hybrid approaches, a series of one-dimensional multicomponent Riemann problems is solved with each of the methods. The solutions are compared with the exact solution to the Riemann problem, and stability of the numerical methods are discussed.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part II: Two-Dimensional Applications

A time-derivative preconditioned system of equations suitable for the numerical simulation of multicomponent/multiphase inviscid flows at all speeds was described in Part I of this paper. The system was shown to be hyperbolic in time and remain well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. Application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces was shown to generate nonphysical pressure and velocity oscillations across the contact surface, which separates the fluid components. It was demonstrated using the one-dimensional Riemann problem that these oscillations may lead to stability problems when the interface separates fluids with large density ratios, such as water and air. The effect of which leads to the requirement of small physical time steps and slow subiteration convergence for the implicit time marching numerical method. Alternatively, the nonconservative and hybrid formulations developed by the present authors were shown to eliminate this nonphysical behavior. While the nonconservative method did not converge to the correct weak solution for flow containing shocks, the hybrid method was able to capture the physically correct entropy solution and converge to the exact solution of the Riemann problem as the grid is refined. In Part II of this paper, the conservative, nonconservative, and hybrid formulations described in Part I are implemented within a two-dimensional structured body-fitted overset grid solver, and a study of two unsteady flow applications is reported. In the first application, a multiphase cavitating flow around a NACA0015 hydrofoil contained in a channel is solved, and sensitivity to the cavitation number and the spatial order of accuracy of the discretization are discussed. Next, the interaction of a shock moving in air with a cylindrical bubble of another fluid is analyzed. In the first case, the cylindrical bubble is filled with helium gas, and both the conservative and hybrid approaches perform similarly. In the second case, the bubble is filled with water and the conservative method fails to maintain numerical stability. The performance of the hybrid method is shown to be unchanged when the gas is replaced with a liquid, demonstrating the robustness and accuracy of the hybrid approach.