Advanced Numerical Method

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The governing equation of fluid dynamics, such as Euler or Naiver-Stokes equation is almost impossible to solve analytically, due to the non-linearity of these equations, thus the computational approach is important. During the past few decades, the computational fluid dynamics (CFD) is widely explored, and recent dramatic development makes it feasible to analyze complex flow physics around realistic aircraft numerically. The radical issue of CFD is the high-fidelity numerical modeling of hyperbolic conservation laws, including these governing equation. Up to now, our laboratory have developed various robust, accurate and efficient numerical methods, such as advanced flux scheme (RoeM, AUSMPW+, M-AUSMPW+) and high resolution scheme reflecting multi-diemsnional effect (MLP).

 

Fig. 1 3-D Viscous Shock Tube Problem

 

The above figure shows the result of three-dimensional viscous shock tube via M-AUSMPW+ and MLP5. The proposed methods is successfully capture a complex vortex structure induced by the interaction of moving and reflecting shock and boundary layer.

 

Fig. 2 Interaction of Shock Wave with 2-D Wedge

 

Fig. 3 Interaction of Shock Wave with 3-D Cone

 

Above animated figure shows the interaction of shock wave with 2-D wedge and 3-D cone. The MLP-u slope limiter implemented on both finite volume method (FVM) and discontinuous Galerkin (DG) method gives enhanced resolution of compressive and non-compressive flow structure during long time unsteady calculation.

We have a strong capability of analyzing a complex flow of realistic air vehicles and its internal components via these high-fidelity approaches.