A one-equation turbulence model for aerodynamic flows

Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

This Key Note presents a summary of the development of the Finite Element Method in the field of Electromagnet ic Engineering, together with a description of several contributions of the authors to the Finite Element Method and its application to the solution of electromagnetic problems. First, a self-adaptive mesh scheme is presented in the context of the quasi-static and full-wave analysis of general anisotropic multiconductor arbitrary shaped waveguiding structures. A comparison between two a posteriori error estimates is done. The first one is based on the complete residual of the differential equations defining the problem. The second one is based on a recovery or smoothing technique of the electromagnetic field. Next, an implementation of the first family of Nedelec's curl-conforming elements done by the authors is outlined. Its features are highlighted and compared with other curl-conforming elements. A presentation of an iterative procedure using a numerically exact radiation condition for the analysis of open (scattering and radiation) problems follows. Other contributions of the authors, like the use of wavelet like basis functions and an implementation of a Time Domain Finite Element Method in the context of two-dimensional scattering problems are only mentioned due to the lack of space.

The finite element method in electromagnetics

A new set of benchmarks has been developed for the performance evaluation of highly parallel supercom puters. These consist of five "parallel kernel" bench marks and three "simulated application" benchmarks. Together they mimic the computation and data move ment characteristics of large-scale computational fluid dynamics applications. The principal distinguishing feature of these benchmarks is their "pencil and paper" specification-all details of these benchmarks are specified only algorithmically. In this way many of the difficulties associated with conventional bench- marking approaches on highly parallel systems are avoided.

/pdf/the-nas-parallel-benchmarks-1v48ldcocu.pdf

The Nas Parallel Benchmarks

We numerically integrate the compressible Navier-Stokes equations by means of a finite volume technique on the domain exterior to an airfoil. The curvilinear grid we use for discretization of the Navier-Stokes equations is obviously finite, it covers only a certain bounded region around the airfoil, consequently, we need to set some artificial boundary conditions at the external boundary of this region. The artificial boundary conditions we use here are non-local in space. They are constructed specifically for the case of steady-state solution. In constructing the artificial boundary conditions, we linearize the Navier-Stokes equations around the far-field solution and apply the difference potentials method. The resulting global conditions are implemented together with a pseudotime multigrid iteration procedure for achieving the steady state. The main goal of this paper is to describe the numerical procedure itself, therefore, we primarily emphasize the computation of artificial boundary conditions and the combined usage of these artificial boundary conditions and the original algorithm for integrating the Navier-Stokes equations. The underlying theory that justifies the proposed numerical techniques will accordingly be addressed more briefly.

External flow computations using global boundary conditions

The aim of this paper is to introduce time-reversed absorbing conditions in time-reversal methods. They enable one to 'recreate the past' without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems: the reduction of the size of the computational domain and the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave and Helmholtz equations illustrate the efficiency of the method. This technique is fairly insensitive to noise in the data.

https://iopscience.iop.org/article/10.1088/0266-5611/27/6/065003/pdf

Time-reversed absorbing condition: application to inverse problems

We consider fourth order accurate compact schemes for numerical solutions to the Maxwell equations. We use the same mesh stencil as used in the standard Yee scheme. In particular extra information over a wider stencil is not required. Hence, it is relatively easy to modify an existing code based on the Yee algorithm to make it fourth order accurate. Also, a staggered mesh makes the boundary treatment easier. Finally, a staggered grid system gives a lower error than a non-staggered system.

Fourth order method for Maxwell equations on a staggered mesh

Phase Error and Stability of Second Order Methods for Hyperbolic Problems. II

An unsteady Reynolds-averaged Navier-Stokes solver is applied for the simulation of a synthetic (zero net mass flow) jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as case 1 for the Computational Fluid Dynamics Validation 2004 (CFDVAL2004) workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous (phase-averaged) data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results from two-dimensional simulations with one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning, and time-step variation are also examined.

Eli Turkel

Papers

External flow computations using global boundary conditions

Time-reversed absorbing condition: application to inverse problems

Fourth order method for Maxwell equations on a staggered mesh

Phase Error and Stability of Second Order Methods for Hyperbolic Problems. II

Simulation of Synthetic Jets Using Unsteady Reynolds-Averaged Navier-Stokes Equations