Author
Robert D. Richtmyer
Bio: Robert D. Richtmyer is an academic researcher from University of Colorado Boulder. The author has contributed to research in topics: Initial value problem & Hyperbolic geometry. The author has an hindex of 11, co-authored 18 publications receiving 13010 citations.
Papers
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4,135Â citations
01 Jan 1967
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
Abstract: Keywords: equations : differentielles ; stabilite ; transport ; transfert de chaleur ; mecanique des : fluides ; ondes Reference Record created on 2005-11-18, modified on 2016-08-08
3,449Â citations
TL;DR: In this paper, the equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks.
Abstract: The equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks. The quantitative influence of these terms can be made as small as one wishes by choice of a sufficiently fine mesh for the numerical integrations. A set of difference equations suitable for the numerical work is given, and the condition that must be satisfied to insure their stabilty is derived.
1,953Â citations
1,696Â citations
673Â citations
Cited by
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TL;DR: In this paper, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
10,727Â citations
TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
8,174Â citations
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
6,630Â citations
Book•
01 Jan 2002TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Abstract: 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.
5,791Â citations
Book•
29 Oct 1999TL;DR: In this paper, Spectral Theory for Semigroups and Generators is used to describe the exponential function of a semigroup and its relation to generators and resolvents.
Abstract: Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.
4,348Â citations