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Circular function-based gas-kinetic scheme for simulation of inviscid compressible flows. (English) Zbl 1349.76752
Summary: This paper presents a new gas-kinetic scheme for simulation of compressible inviscid flows. It starts to simplify the integral domain of Maxwellian distribution function over the phase velocity \(\xi\) and phase energy \(\zeta\) to the integral domain of modified Maxwellian function over the phase velocity \(\xi\) only. The influence of integral over phase energy \(\zeta\) is embodied as the particle internal energy \(e_p\). The modified Maxwellian function is further simplified to a circular function with the assumption that all the particles are concentrated on a circle. Then two circular function-based gas-kinetic schemes are presented for simulation of compressible inviscid flows. In the new schemes, no error and exponential functions, which are often appeared in the Maxwellian function-based gas-kinetic schemes, are involved. As a result, the new schemes can be implemented in a more efficient way. To validate the proposed new gas-kinetic schemes, test examples in the transonic flow, supersonic flow and hypersonic flow regimes are solved. Numerical results showed that the solution accuracy of the circular function-based gas-kinetic schemes is comparable to that of corresponding Maxwellian function-based gas-kinetic schemes. However, the circular function-based gas-kinetic schemes need less computational effort.

76M28 Particle methods and lattice-gas methods
76N15 Gas dynamics (general theory)
76H05 Transonic flows
Full Text: DOI
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