The Research Of Entropy Consistent Schemes Based On Four-order CWENO Reconstruction

With the rapid development of computer science and technology, numerical methods become particularly important for solving hyperbolic conservation laws in computational fluid dynamics. In order to ensure numerical solutions had physical meaning, some numerical methods that satisfy entropy stable condition were developed according to the second law of thermodynamics, such as entropy stable schemes and entropy consistent schemes that were discussed in this thesis. These kind of schemes avoided non-physical phenomenon, such as "expansion shock", "dispersion effect", which has a good application prospect in solving hyperbolic conservation laws. In view of this, some related main ideas and constructed methods for entropy consistent schemes were discussed in detail. Based on the existing entropy consistent scheme, in order to improve the accuracy of numerical schemes, we construct a new scheme by the Fourth Order CWENO type reconstruction for left and right state values in the calculating cell interface. Numerical experiments for inviscid Burgers equation and Euler equations verified the good features of the new scheme when capturing discontinuities, such as high order of accuracy, robustness, essentially non-oscillations. The main work is done as follows:(1) Begin with entropy conservation schemes for solving hyperbolic conservation laws,the development of entropy stable scheme, entropy consistent scheme and high-resolution entropy consistent scheme is particularly introduced. And with each scheme, one dimensional inviscid Burgers equation with discontinuous initial value problem was solved to verify the characteristics of different schemes and effects in capturing discontinuities.(2) A high order accuracy entropy consistent scheme was constructed by combining the Fourth Order CWENO reconstruction for left and right state values in the calculating cell interface and the LeFloch Fourth Order of entropy conservation scheme. Numerical experiments for inviscid Burgers equation illustrated that the new CWENO-type entropy consistent scheme is of the virtues of essentially non-oscillations, high order of accuracy and the high resolution at discontinuities.(3) The high order entropy consistent schemes for Euler equations are constructed.Numerical tests for the Euler Equations also verified the features of the new schemes, such as non oscillation, high precision, high resolution, and robustness.