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- 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)

- 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)

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)

- 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)

We present numerical solutions of weak shock Mach reflections that contain a remarkably complex sequence of supersonic patches, triple points, and expansion fans immediately behind the leading triple point. This structure resolves the von Neumann triple point paradox of weak shock Mach reflection. During the second world war, von Neumann carried out an… (More)

- Allen M. Tesdall, John K. Hunter
- J. Comput. Science
- 2013

We numerically solve a problem for the unsteady transonic small disturbance equations that describes the diffraction of a weak shock into an expansion wave. In the context of a shock moving into a semi-infinite wall, this problem describes the interaction between the reflected part of the shock and the part that is transmitted beyond the wall. We formulate… (More)