In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated with the simulation of the elastic deformation of a wing in subsonic and transonic flow.

Measurement of blood flow rate (Qa) is used to monitor arteriovenous fistulas and grafts that are used for hemodialysis blood access. Most Qa measurements use indicator dilution techniques to measure the recirculation that is induced by the reversal of hemodialysis blood lines. R plus the dialysis circuit flow (Qb) allows the calculation of Qa. The principle of needle reversal also can be used ...

This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

Simulations of turbulent flows are challenging and require tight and varying mesh spacings near the walls that depend on the turbulence models used. Semi-structured meshes are often used in the turbulent wall boundary layers due to their ability to be strongly graded and anisotropic. To reduce the discretization errors in the solution, an adaptive approach becomes essential due to the lack of g...

Two one-sided conservation form difference approximations to a scalar one-dimensional convex conservation law are introduced. These are respectively of first- and second-order accuracy and each has the minimum possible band-width. They are nonlinearly stable, they converge only to solutions satisfying the entropy condition, and they have sharp monotone profiles. No such stable approximation of ...

We obtained global transonic solutions representing optically thin advectiondominated accretion flow by solving the full set of differential equations describing such systems. We found that far from the sonic point self-similar solutions are an excellent approximation of the global flow structure if the accretion rate is well below the maximum value above which no optically thin solutions exist...

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equa...

A pressure-based implicit procedure to solve the Euler and Navier-Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is described. The boundedness criteria for this procedure are determined from Normalized Variable diagram (NVD) scheme.The procedure incorporates the ε−k eddy-viscosity turbulence model. The algorithm is tested for inviscid and turbulent transonic ...

The connection between gas dynamics and differential geometry is discussed. Some history of boundary value problems for systems of conservation laws is first given. Then the mathematical formulation of compressible gas dynamics, especially the subsonic and transonic flows past an obstacle (such as an airfoil), is provided. Some recent results on transonic flow from viscous approximation and com...