Exponential Approximation Space Based Finite Volume WENO Scheme for Solving the Five-equation Model of Compressible Two-medium Flows

In this work, we develop a finite volume weighted essentially non-oscillatory (WENO) scheme based on an exponential approximation space for solving the five-equation transport model of compressible two-medium flows. Compared to the scheme based on the conventional polynomial approximation space, the performance of the present scheme is improved by locally optimizing the shape parameter in the exponential function such that the reconstructed solution can attain one enhanced order of accuracy without the need of increasing the stencil size. More importantly, through analyzing the relationship between the shape parameter and the linear weights of the WENO approximation, we present a suitable upper bound for the shape parameter which is able to avoid the appearance of negative linear weights. Finally, with the aim of maintaining computational robustness under large density and pressure ratios, we design a bound-preserving and positivity-preserving limiting algorithm targeted for the non-polynomial approximation space based finite volume WENO scheme. Numerical results demonstrate that the present scheme achieves high-order accuracy, high resolution and strong robustness in simulating compressible two-medium flows.