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A Time-Accurate Dynamic Mesh Approach For High-Order Shock Computation in Multiple Dimensions
Fujimoto, Takeshi
Fujimoto, Takeshi
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Abstract
A high-order shock-fitting approach has been developed for the two-dimensional Euler equations to compute shock waves with high-order accuracy. A time-accurate dynamic mesh algorithm plays a central role in the approach. A key ingredient of the strategy is a shock detection procedure capable of handling moving shock waves in a high-order simulation. Once shock waves are detected along element interfaces, the shock speed is computed based on the method of characteristics. Then, these interfaces move at the speed of the shock, and an upwind flux for the interfaces automatically guarantees the Rankine-Hugoniot condition. In addition, the entire mesh is deformed to comply with the motion of the shocks to avoid mesh warping and negative Jacobians. In the present study, quadratic (Q2) triangular meshes are employed. This means curved shocks are approximated with quadratic curves, achieving 3rd-order accuracy. The shock-fitting approach is tested for several benchmark problems to demonstrate its performance and accuracy.
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This is the paper from a presentation given at AIAA SciTech on 01/07/2025.
Date
2025-01-07
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University of Kansas
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FujimotoT_2025.pdf
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Keywords
CFD, High-Order-Method, Shock-Fitting, Shock Wave, FR/CPR