A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

Table 3

Comparison of the LB finite difference solutions with exact solution for 𝜈=0.005 with 𝑑𝑥=0.005,𝑑𝑡=0.003, and 𝜏=1.1 at different times.

𝑥	𝑡
	1.4		2.0		2.6
	Numerical	Exact	Numerical	Exact	Numerical	Exact
0.1	0.06303	0.06394	0.04567	0.04621	0.03581	0.03618
0.2	0.11975	0.12784	0.09133	0.09241	0.07162	0.07234
0.3	0.18902	0.19168	0.13694	0.13854	0.10717	0.10826
0.4	0.25091	0.25434	0.17809	0.18022	0.13367	0.13521
0.5	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
0.6	−0.25091	−0.25434	−0.17809	−0.18022	−0.13367	−0.13521
0.7	−0.18902	−0.19168	−0.13694	−0.13854	−0.10717	−0.10826
0.8	−0.12605	−0.12784	−0.09133	−0.09241	−0.07162	−0.07234
0.9	−0.06303	−0.06394	−0.04567	−0.04621	−0.03581	−0.03618