| Numerical simulation has become an extremely important methods for reseaching the fluidmovement. So the study of these methods are very significant. The new adaptive meshnumerical schemes are obtained by combining the adaptive mesh method with high resolutionentropy consistent schemes. These schemes are based on physical point, satisfy the second lawof thermodynamics, which is the entropy stable condition. Meanwhile, these new schemesrealize the combination with the adaptive mesh method and can effectively avoid thenon-physical phenomena, such as expansion shock and negative pressure, etc.. The mainachievements of this work were as follows:(1) Entropy consistent scheme can control entropy production more exactly, so it can eliminatespurious oscillations effectively, and avoid the happening of unphysical expansion shock.Based on this scheme,we introduce limiters, then a high resolution entropy consistentscheme is obtained. Different numerical experiments demonstrated that the scheme could beable to adjust and control the numerical dissipation and dispersion effect.(2) The high resolution entropy consistent scheme was extended to viscous mechanism. Theresults of Navier-Stokes equations (steady shock) demonstrated that the entropy stable andthe entropy consistent sheme adding physical viscous term both can produce correct entropywith proper viscous coefficients and can capture the shock wave sharply.(3) The new adaptive mesh numerical scheme is obtained by combining the adaptive meshmethods with high resolution entropy consistent scheme. The new scheme uses the entropyconservation scheme on smooth sections of the solution, keep the second order accurate.Meanwhile it use the entropy consistent scheme on the discontinuous sections and avoidgenerating the unphysical solution. Numerical experiments showed that this method couldeffectively eliminate expansion shock, can improve the accuracy and resolution. This newscheme is robustness, reliability and no oscillation. |
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