# Highly Accurate Compressible Fluid solver

In fluid mechanics, the flow is considered compressible when the fluid density varies significantly in response to a change in pressure. Compressibility effects are typically considered significant if the Mach number (the ratio of the flow velocity to the local speed of sound) of the flow exceeds 0.3, or if the fluid undergoes very large pressure changes. The most distinct phenomenon associated with high speed flows is the existence of non isentropic solutions or shock waves.

The new compressible solver introduced in LS-DYNA is based on the space-time conservation element and solution element (CE/SE) method, originally proposed by Dr. Chang in NASA Glenn Research Center. It is a new numerical framework for solving conservation laws. The CE/SE method is not an incremental improvement of a previously existing CFD method, and it differs substantially from many other well-established methods. The CE/SE method is a second order explicit scheme and it has many nontraditional features. Some of the most important features include :

- The flux conservation in space AND time (locally and globally) that allows a physical reality to be retained even in regions of discontinuities.
- The spatial derivatives are treated as unknowns rather then discretized which allows highly accurate solutions (more accurate than normal second order schemes).

- A novel and efficient shock capturing strategy that does not use classic Riemann solvers.
- Flexible element shape (e.g., hexahedra, wedges, tetrahedra, ... ).
- Both strong shocks and small disturbances can be handled very well simultaneously.

To date, this method has been used to solve many different types of flow problems, such as detonation waves, shock/acoustic wave interaction, cavitating flows, and chemical reaction flows.