International Journal for Numerical Methods in Fluids

A computational fluid dynamics study of the swimming efficiency of a two‐dimensional flapping hydrofoil at a Reynolds number of 1100 is presented. The model accounts fully for viscous effects that are particularly important when flow separation occurs. The model uses an arbitrary Lagrangian–Eulerian (ALE) method to track the moving boundaries of oscillatory and flapping bodies. A parametric analysis is presented of the variables that affect the motion of the hydrofoil as it moves through the flow along with flow visualizations in an attempt to quantify and qualify the effect that these variables have on the performance of the hydrofoil. Copyright © 2003 John Wiley & Sons, Ltd.

Two‐dimensional initial‐boundary value problems are considered for the shallow water equations and the equation of advection and dispersion of pollutants. The problems are solved in curvilinear boundary fitted co‐ordinates. The transformed equations are integrated on a regular grid by the semi‐implicit and implicit finite difference methods. Based on the numerical method, the integrated modelling system Cardinal for coastal area dynamics and pollution processes is developed for application on personal computers. Examples of computations are given.

In order to investigate the fluid/structure interaction of a bridge deck in a cross wind, a two‐dimensional hp/Spectral fluid solver has been modified to incorporate a body undergoing translational and rotational motion. A moving frame of reference is attached to the body to utilize the efficiency of a fixed mesh solver. The critical reduced velocity at which a bridge deck undergoes a two degree of freedom flutter instability is then predicted using various methods: a theoretical linear potential model; quasi‐steady theory; a linear evaluation of applied forces using prescribed motion; and free translational and rotational motion of the structure. These predictions are compared with experimental data and the various merits of each scheme are reported. Copyright © 2003 John Wiley & Sons, Ltd.

Data assimilation provides techniques for combining observations and prior model forecasts to create initial conditions for numerical weather prediction (NWP). The relative weighting assigned to each observation in the analysis is determined by its associated error. Remote sensing data usually has correlated errors, but the correlations are typically ignored in NWP. Here, we describe three approaches to the treatment of observation error correlations. For an idealized data set, the information content under each simplified assumption is compared with that under correct correlation specification. Treating the errors as uncorrelated results in a significant loss of information. However, retention of an approximated correlation gives clear benefits. Copyright © 2007 John Wiley & Sons, Ltd.

After several years of planning, the 1st International Workshop on High‐Order CFD Methods was successfully held in Nashville, Tennessee, on January 7–8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astronautics, the Air Force Office of Scientific Research, and the German Aerospace Center provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are described. Pacing items requiring further effort are presented. Copyright © 2013 John Wiley & Sons, Ltd.

The Multidimensional Optimal Order Detection (MOOD) method for two‐dimensional geometries has been introduced by the authors in two recent papers. We present here the extension to 3D mixed meshes composed of tetrahedra, hexahedra, pyramids, and prisms. In addition, we simplify the u2 detection process previously developed and show on a relevant set of numerical tests for both the convection equation and the Euler system that the optimal high order of accuracy is reached on smooth solutions, whereas spurious oscillations near singularities are prevented. At last, the intrinsic positivity‐preserving property of the MOOD method is confirmed in 3D, and we provide simple optimizations to reduce the computational cost such that the MOOD method is very competitive compared with existing high‐order Finite Volume methods.Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we resolve the ever‐present confusion over the Quadratic Upwind Interpolation for Convective Kinematics (QUICK) scheme: it is a second‐order scheme or a third‐order scheme. The QUICK scheme, as proposed in the original reference (B. P. Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59‐98), is a third‐order (not second‐order) finite‐volume scheme for the integral form of a general nonlinear conservation law with point‐valued solutions stored at cell centers as numerical solutions. Third‐order accuracy is proved by a careful and detailed truncation error analysis and demonstrated by a series of thorough numerical tests. The QUICK scheme requires a careful spatial discretization of a time derivative to preserve third‐order accuracy for unsteady problems. Two techniques are discussed, including the QUICKEST scheme of Leonard. Discussions are given on how the QUICK scheme is mistakenly found to be second‐order accurate. This paper is intended to serve as a reference to clarify any confusion about third‐order accuracy of the QUICK scheme and also as the basis for clarifying economical high‐order unstructured‐grid schemes as we will discuss in a subsequent paper.

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high‐order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier–Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two‐dimensional Taylor–Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three‐dimensional flow in an air‐conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd.

A number of contributed solutions to the problem of laminar natural convection in a square cavity have been compared with what is regarded as a solution of high accuracy. The purposes of this exercise have been to confirm the accuracy of the bench mark solution and to provide a basis for the assessment of the various methods and computer codes used to obtain the contributed solutions.

A two‐dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first‐order upwind technique, a second order in space and time and an extended first‐order method are applied to solve the non‐diffusive terms in both the flow and solute equations and a centred implicit discretization is applied to the diffusion terms. The stability constraints are studied and the form to avoid oscillatory results in the solute concentration in the presence of complex flow situations is detailed. Some comparisons are carried out in order to show the performance in terms of accuracy of the different options. Copyright © 2007 John Wiley & Sons, Ltd.