Space-Time Conservation Element and Solution Element (CE/SE)

Taitech CFD scientists are working with NASA scientists to develop the CE/SE computational methodology. This code is now used by NASA, the Air Force and several universities studying aero acoustics and simulating pulse detonation engine performance. The CE/SE method can be applied to a wide spectrum of flows, from weak acoustic waves to discontinuous shock waves. It is ideal for application in both CFD and Computational Aero-Acoustics (CAA). Salient properties of the CE/SE Method are:

1. Both local and global flux conservations are enforced in space and time instead of in space only.
2. All independent variables and their spatial derivatives are considered as individual unknowns to be solved for simultaneously at each grid point.
3. The CE/SE method is based on a non-dissipative scheme with addition of fully controllable numerical dissipation.
4. The flux-based specification of the CE/SE scheme gives rise in a natural fashion to a simple yet general non-reflecting boundary condition which is an important issue in computational aero-acoustics.

Practical advantages of the CE/SE methodology over other high order finite difference methods are as follows:

1. It is robust, with high resolution and low dispersion and dissipation
2. It is naturally adapted to unstructured grid (truly multidimensional flux).
3. It is a novel, simple technique with robust Non-Reflecting Boundary Condition (NRBC).
4. It has the most compact stencil. This leads to efficient parallel computing and easy implementation of boundary conditions, e.g., robust Non-Reflecting Boundary Condition (NRBC).
5. It can capture shocks accurately without using Riemann solvers or dimensional-splitting techniques.

Recent Success Story: In April 2001, the CE/SE scheme was used by Taitech researchers to solve the NASA acoustic benchmark problem.

Also see http://www.lerc.nasa.gov/WWW/microbus/