# The Space-Time Conservation Element and Solution Element (CESE) Method

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The space-time conservation element and solution element (CESE) method is a novel numerical method developed by Sin-Chung Chang for time-accurate, high-fidelity solution of hyperbolic partial different equations or conservation laws:

Key features of the CESE method include:

Temporal coordinate is treated in the same way as spatial coordinates for calculating space-time fluxes.

The method solves the integral form of the equations.

The method uses staggered space-time mesh.

Unstructured meshes are intrinsically used in multi-dimensional space.

The method is mathematically simple. Time-marching algorithms are based on enforcing space-time flux conservation.

No Riemann solver is used.

The gradients of solution are also independent unknowns.

The Jacobian matrices in the first-order formulation fully characterize the equations to be solved.

Consequently, the CESE method provides the following merits:

Nonlinearity is easily accommodated. Shock-capturing is accurate and robust.

The explicit time-marching algorithms are straightforward and efficient in terms of operation count.

Complex geometry can be easily fit by using unstructured meshes with mixed shapes.

The method is ideal for parallel computing.

The method is generic to all conservation laws, i.e., changing solely the Jacobian matrices changes the equations to be solved.

The method provides simple and effective treatments for non-reflective boundary conditions.

## External links

Yazhong Jiang, Chih-Yung Wen and Deliang Zhang,

*Space–Time Conservation Element and Solution Element Method and Its Applications*, AIAA Journal, Volume 58, Number 12, December 2020, Page 5408-5430. DOI: 10.2514/1.J058928Ohio State Computational Fluid Dynamics Laboratory Research page (archived)