A New Positivity-Preserving Technique for High-Order Schemes to Solve Extreme Problems of Euler Equations on Structured Meshes

In this paper, we propose a new positivity-preserving (new PP) technique for fifth-order finite volume unequal-sized WENO schemes when solving some extreme problems of compressible Euler equations on structured meshes. After spatial reconstruction in each time marching, a detective process is used to examine the positivity of density and pressure at some checking points in each target cell. If the negativity happens at one checking point, a new compression limiter is carried out to ensure that the modified polynomials can achieve the positivity of density and pressure in the whole target cell instead of only at some discrete points. This treatment is easily implemented, owing to a quick and simple way to overestimate the minimum and maximum values of the polynomials of density and pressure in the target cell. Some numerical experiments for classical extreme problems show that the proposed method has an advantage in computational efficiency and robustness in comparison to the classical positivity-preserving techniques (Zhang and Shu in J Comput Phys 229:8918–8934, 2010), since the CFL number of 0.6 is allowed for all tests in this paper.