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- Barbara Lee Keyfitz, Sunčica Čanić, +5 authors David Wagner
- 2002

- Allen M. Tesdall, John K. Hunter
- SIAM Journal of Applied Mathematics
- 2002

We present numerical solutions of a two-dimensional Riemann problem for the unsteady transonic small disturbance equations that provides an asymptotic description of the Mach reflection of weak shock waves. We develop a new numerical scheme to solve the equations in self-similar coordinates and use local grid refinement to resolve the solution in the… (More)

An asymptotic analysis of the regular and Mach reflection of weak shocks leads to shock reflection problems for the unsteady transonic small disturbance equation. Numerical solutions of this equation resolve the von Neumann triple point paradox for weak shock Mach reflection. Related equations describe steady transonic shock reflections, weak shock… (More)

- Oliver Kreylos, Allen M. Tesdall, B. Hamanny, John K. Hunter, Kenneth I. Joy
- VisSym
- 2002

We describe a system that supports real-time interactive visualization of computational fluid dynamics (CFD) simulations. The system allows a user to place and manipulate visualization primitives, such as isolines and streamlines, during an ongoing simulation process. A user can interactively select and designate regions of the computational mesh for… (More)

- Allen M. Tesdall, Richard Sanders, Barbara L. Keyfitz
- SIAM Journal of Applied Mathematics
- 2006

We present numerical solutions of a two-dimensional Riemann problem for the non-linear wave system which is used to describe the Mach reflection of weak shock waves. Robust low order as well as high resolution finite volume schemes are employed to solve this equation formulated in self-similar variables. These, together with extreme local grid refinement,… (More)

- John K. Hunter, Allen M. Tesdall
- SIAM Journal of Applied Mathematics
- 2012

We study an asymptotic problem that describes the diffraction of a weak, self-similar shock near a point where its shock strength approaches zero and the shock turns continuously into an expansion wavefront. An example arises in the reflection of a weak shock off a semi-infinite screen. The asymptotic problem consists of the unsteady transonic small… (More)

- Allen M. Tesdall, Richard Sanders, Barbara L. Keyfitz
- SIAM Journal of Applied Mathematics
- 2008

We present numerical solutions of a two-dimensional Riemann problem for the com-pressible Euler equations that describes the Mach reflection of weak shock waves. High resolution finite volume schemes are used to solve the equations formulated in self-similar variables. We use extreme local grid refinement to resolve the solution in the neighborhood of an… (More)

- IN GASDYNAMICS, ALLEN M. TESDALL, BARBARA L. KEYFITZ
- 2008

We present numerical solutions of a two-dimensional Riemann problem for the com-pressible Euler equations that describes the Mach reflection of weak shock waves. High resolution finite volume schemes are used to solve the equations formulated in self-similar variables. We use extreme local grid refinement to resolve the solution in the neighborhood of an… (More)

We present numerical solutions of the steady and unsteady transonic small disturbance equations that describe the Mach reflection of weak shock waves. The solutions contain a complex structure consisting of a sequence of triple points and tiny supersonic patches directly behind the leading triple point, formed by the reflection of weak shocks and expansion… (More)

- Allen M. Tesdall, Richard Sanders, Nedyu Popivanov
- J. Sci. Comput.
- 2015

Recent numerical solutions and shock tube experiments have shown the existence of a complex reflection pattern, known as Guderley Mach reflection, which provides a resolution of the von Neumann paradox of weak shock reflection. In this pattern, there is a sequence of tiny supersonic patches, reflected shocks and expansion waves behind the triple point, with… (More)