Robert V. Wilson

Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures

We present a comprehensive approach to verification and validation methodology and procedures for CFD simulations from an already developed CFD code applied without requiring availability of the source code for specified objectives, geometry, conditions, and available benchmark information. Concepts, definitions, and equations derived for simulation errors and uncertainties provide the overall mathematical framework. Verification is defined as a process for assessing simulation numerical uncertainty and, when conditions permit, estimating the sign and magnitude of the numerical error itself and the uncertainty in that error estimate. The approach for estimating errors and uncertainties includes (1) the option of treating the numerical error as deterministic or stochastic, (2) the use of generalized Richardson extrapolation for J input parameters, and (3) the concept of correction factors based on analytical benchmarks, which provides a quantitative metric to determine proximity of the solutions to the asymptotic range, accounts for the effects of higher-order terms, and are used for defining and estimating errors and uncertainties

Comprehensive Approach to Verification and Validation of CFD Simulations—Part 2: Application for Rans Simulation of a Cargo/Container Ship

Part 2 of this two-part paper provides an example case study following the recently developed comprehensive verification and validation approach presented in Part 1. The case study is for a RANS simulation of an established benchmark for ship hydrodynamics using a ship hydrodynamics CFD code. Verification of the resistance (integral variable) and wave profile (point variable) indicates iterative uncertainties much less than grid uncertainties and simulation numerical uncertainties of about 2%S 1 (S1 is the simulation value for the finest grid). Validation of the resistance and wave profile shows modeling errors of about 8%D (D is the measured resistance) and 6% z max (z max is the maximum wave elevation), which should be addressed for possible validation at the 3%D and 4%z max levels. Reducing the level of validation primarily requires reduction in experimental uncertainties. The reduction of both modeling errors and experimental uncertainties will produce verified and validated solutions at low levels for this application using the present CFD code. Although there are many issues for practical applications, the methodology and procedures are shown to be successful for assessing levels of verification and validation and identifying modeling errors in some cases. For practical applications, solutions are far from the asymptotic range; therefore, analysis and interpretation of the results are shown to be important in assessing variability for order of accuracy, levels of verification, and strategies for reducing numerical and modeling errors and uncertainties. @DOI: 10.1115/1.1412236#

Numerical simulation of turbulent jets with rectangular cross-section

Three-dimensional turbulent jets with rectangular cross-section are simulated with a finite-difference numerical method. The full Navier-Stokes equations are solved at low Reynolds numbers, whereas at the high Reynolds numbers filtered forms of the equations are solved along with a subgrid scale model to approximate effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporal discretization and a fourth-order compact scheme is used for spatial discretization. Computations are performed for different inlet conditions which represent different types of jet forcing. The phenomenon of axis-switching is observed, and it is confirmed that this is based on self-induction of the vorticity field. Budgets of the mean streamwise velocity show that convection is balanced by gradients of the Reynolds stresses and the pressure.

Higher-order compact schemes for numerical simulation of incompressible flows. Part I: theoretical development

A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization. New insights are presented on the elimination of the odd-even decoupling problem in the solution of the pressure Poisson equation. For consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization. New insights are presented on the elimination of the odd-even decoupling problem in the solution of the pressure Poisson equation. For consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.

URANS simulations for a high-speed transom stern ship with breaking waves

An exploratory study of high-speed surface ship flows is performed to identify modelling and numerical issues, to test the predictive capability of an unsteady RANS method for such flows, to explain flow features observed experimentally, and to document results obtained in conjunction with the 2005 ONR Wave Breaking Workshop. Simulations are performed for a high-speed transom stern ship (R/V Athena I) at three speeds Froude number (Fr) = 0.25, 0.43 and 0.62 with the URANS code CFDSHIP-IOWA, which utilizes a single-phase level set method for free surface modelling. The two largest Fr are considered to be high-speed cases and exhibit strong breaking plunging bow waves. Structured overset grids are used for local refinement of the unsteady transom flow at medium speed and for small scale breaking bow and transom waves at high-speeds. All simulations are performed in a time accurate manner and an examination of time histories of resistance and free surface contours is used to assess the degree to which the solutions reach a steady state. The medium speed simulation shows a classical steady Kelvin wave pattern without breaking and a wetted naturally unsteady transom flow with shedding of vortices from the transom corner. At higher speeds, the solutions reach an essentially steady state and display intense bow wave breaking with repeated reconnection of the plunging breaker with the free surface, resulting in multiple free surface scars. The high-speed simulations also show a dry transom and an inboard breaking wave, followed by outboard breaking waves downstream. In comparison to an earlier dataset, resistance is well predicted over the three speeds. The free surface predictions are compared with recent measurements at the two lowest speeds and show good agreement for both non-breaking and breaking waves.

HIGHER-ORDER COMPACT SCHEMES FOR NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS, PART II: APPLICATIONS

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.A higher-order-accurate numerical procedure, developed for solving incompressible Navier?Stokes equations for 2-D or 3-D fluid flow problems and presented in Part I, is validated. The procedure, which is based on low-storage Runge?Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization, is shown to eliminate the odd?even decoupling problem on regular grids, provided that compact schemes are used to approximate the Laplacian of the pressure equation. Spatial and temporal accuracy are confirmed formally through application to several pertinent benchmark problems. Stability in long-time integration is demonstrated by application to the Stuart?s mixing-layer problem.

Simulation of surface ship dynamics

We present a summary of the three-year Challenge Project (C68), begun in 2001, with the objective of demonstrating a capability to simulate time-dependent six-degree-of-freedom motions of ships in waves and the associated near-field flow using unsteady Reynolds-Averaged Navier-Stokes (RANS) codes. The efforts involved a team of researchers using two state-of-the-art unsteady RANS codes for a progression of building-block simulations at both model- and full-scales and for practical configurations including detailed resolution of propulsors and appendages. The two RANS codes used for this project are UNCLE, developed at the Mississippi State University, and CFDSHIP-IOWA, developed at the University of Iowa. The three-year efforts have successfully demonstrated a capability to simulate coupled pitch/heave motions, coupled pitch/heave/roll motions, maneuvers in the horizontal plane, and near-field wake, including propeller and viscous effects. The predictive capability demonstrated in this project has clearly paved the way for more challenging computations that involve large-amplitude motions in high sea states for a new generation of naval ships, including surface combatant and other future hull forms.

TWO-DIMENSIONAL SPATIALLY DEVELOPING MIXING LAYERS

Two-dimensional, incompressible, spatially developing mixing layer simulations are per formed with two classes of perturbations applied at the inlet boundary: (1) combinations of discrete modes from linear stability theory, and (2) a broad spectrum of modes derived from experimentally measured velocity spectra. The discrete modes from linear theory are obtained by solving the Orr-Sommerfeld equation, and linear stability analysis is used to investigate the effect of Reynolds number on the stability of mixing layers. Two-point spatial velocity and autocorrelations are used to estimate the size and lifetime of the resulting coherent structures and to explore possible feedback effects. It is shown that by forcing with a broad spectrum of modes derived from an experimental energy spectrum, many experimentally observed phenomena can be reproduced by a two-dimensional simulation.

A Parallel Universal Mesh Deformation Scheme

Many approaches for moving and deforming mesh have been developed, but the approach adopted often depends on both the meshing scheme and the proposed application. Approaches based on a spring analogy with linear torsional springs or solution of partial differential equations have been used, but are generally very expensive to solve at each time step and are not trivial to parallelize. Here, a universal approach to g rid motion known as the algebraic interpolation method (AIM) is followed to manage deforming surfaces. This method is universal and applicable to any grid type. Also , it is perfectly suitable to a parallel platform and can be implemented efficiently. The original scheme has some difficulty handling two-node bending mesh deformation involved in various fluid -structure interaction problems and other cases in which mesh deformation is driven solely by the surface motion. Several modifications have been made for these applications. It is determined that the grid quality can be improved significantly by adding a smoothing algorithm. Extra connectivities can also help improve the grid quality. The current scheme is applied to several well known synthetic jet applications from a NASA Langley Workshop for validation. Results are presented for the mesh deformation of NACA0012 airfoil and Suboff body. Free surface evolution of S175 container ship is also included along with its two -node bending mesh deformation.

Pressure calibration of infrared gas analyzers

Abstract The operation principle and some typical calibration techniques of an infrared gas analyzer (IRGA) are discussed. A method for eliminating the influence of pressure broadening of absorption lines during pressure calibration of such an instrument is presented.