Relaxation-rate formula for the entropic lattice Boltzmann model<xref rid="cpb_28_11_114701fn1" ref-type="fn">*</xref><fn id="cpb_28_11_114701fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11471185, 11801030, and 11861131004).</p></fn>

Relaxation-rate formula for the entropic lattice Boltzmann model**

Project supported by the National Natural Science Foundation of China (Grant Nos. 11471185, 11801030, and 11861131004).

Zhao Weifeng¹, Yong Wen-An^{2, †}

(a) The exact density profile for the shock tube problem at time t = 500. The initial state is ρ(0 ≤ x ≤ 400) = 1.5, ρ(400 < x ≤ 800) = 0.75, and u(0 ≤ x ≤ 800) = 0. (b) Distributions of α with viscosity ν = 10⁻⁵ at the compressive shock front from formula (10) (red solid line) and the first-order EELBM (black dashed line).