CESE
The *CESE keyword cards provide input for the Conservation Element/Solution Element (CESE) solver. This method is a novel numerical framework for conservation laws. It has many nontraditional features, including a unified treatment of space and time, the introduction of conservation element (CE) and solution element (SE), and a novel shock capturing strategy without using a Riemann solver. 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. In LSDYNA, it has been extended to also solve fluidstructure interaction problems with the embedded (or immersed) boundary approach or moving (or fitting) mesh approach.
At t=0, an air chamber with high temperature and high pressure gaz is released propelling a projectile at high velocity. This case uses the axisymmetric CESE solver is order to reduce the calculation times.

It is possible to combine the keyword LOAD_BLAST_ENHANCED with the CESE solver in order to achieve an accurate tracking of the pressure loads and pressure wave propagation due to the detonation of a conventional explosive.

This examples features a simple immersed FSI example. The active structure needs to be entirely embedded in the fluid for the immersed method. Interfaces are tracked automatically. It is advised to use a finer mesh for the fluid than for the solid. For FSI problems, the two solvers will use a synchronized timestep i.e the smallest value computed from their respective domains (CFL condition). No leakage can occur.

This examples features a simple CESE input deck coupled with a structural problem. An incoming pressure wave hits a thin plate. Under the load, the elements get progressively eroded allowing the fluid to flow through.

This LSDYNA simulation shows a simple 2D CESE input deck with a diffraction moving normal shock wave around a 90 degree corner. The Mach number is 1.2 and the moving normal shock wave relations are used in order to determine the inlet parameters.

This test case consists of an oblique shock wave impacting a solid wall. The flow is considered viscous meaning
that a boundary layer will be generated on the solid wall which will result in complex interactions occurring between
the oblique shock wave and the boundary layer.

An initially loaded spring is released at t=0. A compression wave is formed in the fluid that bounces back and interacts with the structure thus creating an oscillatory system. In this example, the moving mesh technique is used for FSI rather than the classic embedded approach.

This is a classic 1D model, introduced by G.A. Sod [2] and its purpose is to verify the ability
of the CESE solver to solve fluid dynamics problems with shock wave behavior.
[2] G. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic
conservation laws, J. Comput. Phys., (1978).

The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA, former NASA) in the 1940s. The four digit series define the profile by describing its maximum camber, the location of the maximum camber and the airfoil’s maximum thickness. The NACA 0012 is a symmetrical airfoil frequently used for benchmarking test cases.
