Analysis and applications of the upwind conservation element and solution element scheme for compressible flow simulations

TL;DR

This paper analyzes the upwind CESE scheme's numerical properties and demonstrates its high-resolution capabilities in simulating complex compressible flow phenomena, including shocks and interfaces.

Contribution

The paper provides a formal analysis of the upwind CESE scheme's accuracy, dissipation, and dispersion, and validates its effectiveness through various flow simulations.

Findings

The scheme accurately captures shock waves and interfaces.

Theoretical analysis confirms the scheme's order of accuracy.

Simulation results agree with exact solutions and experimental data.

Abstract

The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled scheme, a formal analysis is conducted on the upwind CESE discretization applied to the linear advection problem. The modified equation and the effective modified wavenumber are derived, which theoretically confirm the order of accuracy and reveal the dissipation and dispersion properties of this scheme. Several examples are considered to demonstrate the capabilities of the upwind CESE scheme for simulating compressible flows, including shock-vortex and shock-bubble interactions. The results of the present scheme agree well with exact solutions, results of other numerical methods, and experimental data. This demonstrates the high resolution of the scheme in capturing shock waves, material interfaces, and small-scale flow structures.