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 propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to ﬁnd a stencil suitable even in the presence of high wavenumbers. The proposed scheme incorporates physically informed elements from the ﬁeld of optimized numerical schemes into a convolutional optimization machine learning algorithm.

A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation

Damage and failures in high-pressure equipment and in high-energy piping have increased significantly during the second part of the twentieth century, in spite of improved construction procedures and the high quality of materials used. The result has been a grave expansion in the number of fatal disasters and ecological catastrophes, and their harmful social and economic consequences. This trend is apparent from a brief analysis of extensively developing industrial activities in different countries of the world, such as chemical, refinery and gas-treatment enterprises, power and the nuclear power industry. The statistics of failures in these industries show that most of the damage was caused by systems of interacting flaws.

Solution of a Dynamic Main Crack Interaction with a System of Micro-Cracks by the Element Free Galerkin Method

The fluctuating field of a jet excited by transient mass injection is simulated numerically The model is developed by expanding the state vector as a mean state plus a fluctuating state Nonlinear terms are not neglected and the effect of nonlinearity is studied The results show a significant spectral broadening in the flow field due to the nonlinearity In addition, large scale structures are broken down into smaller scales

/pdf/simulation-of-the-fluctuating-field-of-a-forced-jet-ui3d816snb.pdf

Simulation of the fluctuating field of a forced Jet

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. One of these schemes reduces to a Runge-Kutta type formula when the equations are linear. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. The averaging procedure advocated by Gragg does not increase the efficiency of the scheme. For parabolic problems severe stability restrictions are encountered that limit the applicability to problems with large cell Reynolds number. Computational results are presented confirming the analytic discussions.

Extrapolation methods for dynamic partial differential equations

: A computer code for hydrodynamic and elastic-perfectly plastic problems is described. The model uses a second order finite difference method based upon a Eulerian formulation of the basic differential equations. The algorithm uses an individual grid for each material domain, determined by Lagrangian type boundary points which are subject to free surface and interface conditions. The only communication between domains is through their common interfaces.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA016944&Location=U2&doc=GetTRDoc.pdf

Eli Turkel

Papers

A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation

Solution of a Dynamic Main Crack Interaction with a System of Micro-Cracks by the Element Free Galerkin Method

Simulation of the fluctuating field of a forced Jet

Extrapolation methods for dynamic partial differential equations

SMITE - A Second Order Eulerian Code for Hydrodynamic and Elastic-Plastic Problems