NUMERICA, is a library of source codes for solving hyperbolic partial differential equations using a broad range of modern, high resolution shock capturing conservative and non-conservative numerical methods. Most of the programs are based on upwind schemes of the Godunov and Flux Vector Splitting type but also included are centred flux and slope limiter TVD methods. Exact and several approximate Riemann solvers form the basic routines of the many schemes of first and higher order of accuracy included in the library.
The selection of approximate Riemann solvers contains: Roe's Riemann solver with the Harten and Hyman entropy fix, Osher's Riemann solver with both the original and the physical ordering of integration paths, the Harten-Lax-van Leer Riemann solver (HLL) in conjunction with several ways of providing wave speed estimates, the HLLC Riemann solver (a modification of HLL to resolve contact discontinuities and shear waves), Two-Shock type Riemann solvers, Primitive Variable Riemann solvers and Adaptive Riemann solvers. Three types of Flux Vector Splitting methods are also included, following the splittings of Steger and Warming, van Leer and the more recent splitting due to Liou and Steffen. Programs for TVD schemes to solve time-dependent problems in one, two and three space dimensions, in Cartesian and body-fitted coordinates, using split and unsplit finite volume schemes, are included.
The exact Riemann solver is a stand-alone program set up for solving Riemann problems for any choice of physically realistic data. This program is most useful in providing exact solutions to partially validate numerical methods. The exact Riemann solver is also used in conjunction with the Random Choice method (or Glimm's method) and the Godunov first order upwind method.
* HYPER-LIN (Version 1.0 ISBN 0-9536483-0-3) is a selection of 20 source codes for solving hyperbolic models equations, such as the linear advection equation, the inviscid Burgers's equation, the linearised equations of gas dynamics and the linearised shallow water equations. HYPER-LIN is highly suitable for teaching purposes and for self studying numerical methods of the high resolution type.
* HYPER-EUL (Version 1.0 ISBN 0-9536483-3-8) is a set of 18 source codes for solving the time dependent Euler equations in one, two and three space dimensions, for both Cartesian and non-Cartesian geometries. This part of NUMERICA is suitable for teaching final year undergraduate and post graduate students in science and engineering. It is most suitable for researchers wishing to use modern numerical methods from first principles. HYPER-EUL is also suitable for developing application software to solve complex scientific and industrial problems.
* HYPER-WAT (Version 1.0 ISBN 0-9536483-5-4) is a selection of 13 source codes for solving the nonlinear, time dependent shallow water equations in one and two space dimensions for both Cartesian and non-Cartesian geometries. Included is a program that solves exactly the Riemann problem for the shallow water equations for all possible physically admissible initial conditions, including the three dry-bed cases that may arise.
* PhD Students in Science and Engineering embarking on a research programme requiring the use of accurate and robust numerical methods from first principles are the prime beneficiaries of NUMERICA. Students will get a quick and firm start in their research and avoid the time-consuming and often chaotic full navigation through hundreds of research papers published in dozens of journals, books and conference proceedings. Numerical analysts in Mathematics Departments will find the source codes a good starting point in their research, for both assessing existing schemes and for implementing new schemes in the frame of the NUMERICA source codes; modifications may consist of adding new subroutines and translating the programs to different programming languages.
* Research Supervisors. Given the current nature of the subject of numerical methods, supervisors will often have no option but to take on research students who have an inadequate background or no background at all. One year or longer is what would normally take to partially remedy this situation. NUMERICA gives supervisors the means to ensure a quick and cost effective start in the research; supervisors may guide their students in the study, assessment and adaptation of selected source programs to solve the problems of their particular interest, ensuring complete control over the development of the project by avoiding the black-box approach. The NUMERICA codes may also be used to provide reference solutions, in order to systematically assess the suitability of all-purpose industrial packages, if these are to be an essential component of the research.
* Academics teaching numerical methods to final year undergraduate and post-graduate students will also find NUMERICA a useful educational tool in providing a valuable practical element to their formal lectures. Practical assignments may involve the use of selected codes to assess the performance of particular numerical methods under a selection of initial and boundary conditions. Students may also be asked to introduce minor (or major) changes to a selected code to study a particular physical problem of interest. Selected codes may form the basis of practical mini-projects and assignments.
* Research Scientists in Academe, Industry, Research Laboratories and Consultancy Organisations will find in NUMERICA a useful solid basis for developing accurate and robust customised software for ambitious practical applications.
Sound documentation, support and continuity are distinctive features of NUMERICA that will give users confidence and peace of mind. The algorithms and their theory are fully documented in textbooks and articles written by the authors of the codes, see references below. Direct support to users is provided by the authors of the codes, through an email based inquiry desk and through regular and on-demand short training courses on NUMERICA and related topics.
NUMERICA will be maintained, regularly upgraded and extended. Planned extensions of the library are to include new sub-libraries written by other authors. Our aim is to widen the range of equations, numerical methods and applications to be included.
* E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, Berlin/Heidelberg/New York, 1997, ISBN 3-540-65966-8. Second edition 1999.
* E. F. Toro and J. F. Clarke (Editors), Numerical Methods for Wave Propagation. Kluwer Academic Publishers, Dordrecht/Boston/London, 1998, ISBN 0-7923-5125-8.
* E. F. Toro, Shock-Capturing Methods for Free-Surface Shallow Flows. John Wiley and Sons, Chichester, 2001, ISBN 0-471-98766-2.
* E. F. Toro (Editor), Godunov Methods: Theory and Applications. Edited Review. Kluwer Academic/Plenum Publishers, 2001.
Three programs from NUMERICA are freely available to you subject to conditions.
They are e1rpexf.f (from the HYPER-EUL
sub-library), bugod.f (from HYPER-LIN)
and swrpex.f (from HYPER-WAT).
Register for the these programs via the link below:
Free Sample Programs Application Form
Once you have registered and have obtained a password, you may access the programs via
the following link:
Futher information available: Product Pricing, Licence Conditions and Support Conditions .
Eight programs from NUMERICA form the Trial version are available to you on request only subject to Licence Conditions. Four of the programs are taken from the sub-library HYPER-LIN ( lawaf.f, bumus.f, gamus.f and swwaf.f) and four from HYPER-EUL ( e1godf.f, e2wafns.f, e2slins.f and e3wafcu.f). In order to access these programs please contact numerica@numeritek.com.
Futher information available: Product Pricing, Licence Conditions and Support Conditions.
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