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The instruction blocks comprise four different coloured pieces: forward, to move the bot forward; left; right; and the green circular function block.
Since the simple distribution function is defined on the circle, for simplicity, it is termed as circular function hereafter.
The modified Maxwellian function is further simplified to a circular function with the assumption that all the particles are concentrated on a circle.
It was shown in [6] that for a circular function f on H n ∖ { e }, we have K ( f ) ( ξ − 1 ) = f , for all ξ ∈ H n ∖ { e } with N = 1.
The pinched-cone equation uses a circular function with one or two coefficients that describe the slope-azimuth-dependent expansion of the pinched cone as snow depth differentiation increases with increased terrain slope.
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Then two circular function-based gas-kinetic schemes are presented for simulation of compressible inviscid flows.
However, the circular function-based gas-kinetic schemes need less computational effort.
The present work is the extension of our previous work [20], where the circular function-based gas-kinetic scheme is presented to simulate inviscid flows.
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.
Numerical results showed that the circular function-based gas-kinetic scheme can provide accurate numerical results with the same computational cost as that needed by conventional Navier Stokes solver.
All our construction, therefore, will work for the class of circular functions only.
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