The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with sma...The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.展开更多
A comparative analysis on the schemes for exact lattice Boltzmann(LB)evolution equation is presented in this paper.It includes two classical exact LB schemes,i.e.,Bosch-Karlin(BK)scheme and He-Luo(HL)scheme,and the pr...A comparative analysis on the schemes for exact lattice Boltzmann(LB)evolution equation is presented in this paper.It includes two classical exact LB schemes,i.e.,Bosch-Karlin(BK)scheme and He-Luo(HL)scheme,and the present Taylor-expansion(TE)scheme.TE scheme originates from the extension of BK scheme.The mathematical mechanism and the equilibrium distribution evolution behind these exact schemes have been detailedly addressed.After that,an analysis is carried out to discuss the cause of the LB equation difference among the schemes,which offers an insight of the exactness in these schemes and brings up their continuity precondition.At last,the schemes are systematically addressed for their pros and cons in the further development of LB equations.展开更多
基金Project supported by National Natural Science Foundation of China.
文摘The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.
基金the National Science and Technology Major Project of China(No.2017ZX06002002)。
文摘A comparative analysis on the schemes for exact lattice Boltzmann(LB)evolution equation is presented in this paper.It includes two classical exact LB schemes,i.e.,Bosch-Karlin(BK)scheme and He-Luo(HL)scheme,and the present Taylor-expansion(TE)scheme.TE scheme originates from the extension of BK scheme.The mathematical mechanism and the equilibrium distribution evolution behind these exact schemes have been detailedly addressed.After that,an analysis is carried out to discuss the cause of the LB equation difference among the schemes,which offers an insight of the exactness in these schemes and brings up their continuity precondition.At last,the schemes are systematically addressed for their pros and cons in the further development of LB equations.
