Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Table 1

Comparison between numerical solutions and the exact solution.

𝑥	FEMLSF	FEMQSF	Exact [19]	RK4-CD6 [19]		MC-CD6
	[30]	[30]		Δ𝑡=10 s	Δ𝑡=1 s	Δ𝑡=10 s	Δ𝑡=1 s
0	1.000	1.000	1.000	1.000	1.000	1.000	1.000
18	1.000	1.000	1.000	1.000	1.000	1.000	1.000
19	1.000	1.000	0.999	0.999	0.999	0.999	0.999
20	0.999	1.000	0.998	0.998	0.998	0.998	0.998
21	0.997	0.999	0.996	0.996	0.996	0.996	0.996
22	0.993	0.996	0.991	0.992	0.991	0.991	0.991
23	0.985	0.989	0.982	0.982	0.982	0.982	0.982
24	0.970	0.974	0.964	0.965	0.964	0.965	0.964
25	0.943	0.946	0.934	0.936	0.935	0.936	0.935
26	0.902	0.900	0.889	0.891	0.889	0.891	0.889
27	0.842	0.832	0.823	0.827	0.824	0.827	0.824
28	0.763	0.743	0.738	0.743	0.739	0.743	0.739
29	0.666	0.638	0.636	0.641	0.637	0.642	0.637
30	0.556	0.524	0.523	0.528	0.523	0.529	0.523
31	0.442	0.411	0.408	0.413	0.408	0.414	0.408
32	0.332	0.306	0.301	0.306	0.301	0.306	0.301
33	0.235	0.218	0.208	0.212	0.208	0.213	0.208
34	0.156	0.147	0.135	0.138	0.135	0.138	0.135
35	0.096	0.095	0.082	0.084	0.082	0.084	0.082
36	0.055	0.058	0.046	0.048	0.047	0.048	0.047
37	0.030	0.034	0.024	0.025	0.025	0.025	0.025
38	0.015	0.019	0.012	0.012	0.012	0.012	0.012
39	0.007	0.010	0.005	0.006	0.005	0.006	0.005
40	0.003	0.005	0.002	0.002	0.002	0.002	0.002
41	0.001	0.003	0.001	0.001	0.001	0.001	0.001
42	0.000	0.001	0.000	0.000	0.000	0.000	0.000
CPU time (s)				0.13	0.86	0.12	0.76
𝐿2 norm error				0.0142	0.0017	0.0148	0.0017
𝐿∞ norm error				0.0055	0.0008	0.0060	0.0008