TY - JOUR

T1 - Renormalization-group theory for the modified porous-medium equation

AU - Chen, Lin Yuan

AU - Goldenfeld, Nigel

AU - Oono, Y.

PY - 1991

Y1 - 1991

N2 - We analyze the long-time behavior of the modified porous-medium equation tu=Du1+n in d dimensions, where n is arbitrary and D=1 for tu>0 and D=1 for tu<0. This equation describes inter alia the height of a groundwater mound during gravity-driven flow in porous media (d=2, n=1) and the propagation of strong thermal waves following an intense explosion (d=3, n=5). Using general renormalization-group (RG) arguments, we show that a radially symmetric mound exists of the form u(r,t)t-(d)f(rt-(), ), where ==1/(2+nd) and and are -dependent anomalous dimensions, obeying the scaling law n(1-nd)=0. We calculate and to O(), for general d and n, using a perturbative RG scheme. In the case of groundwater spreading, our results to O(2) are in good agreement with numerical calculations, with a relative error in the anomalous dimension of about 3% when is 0.5.

AB - We analyze the long-time behavior of the modified porous-medium equation tu=Du1+n in d dimensions, where n is arbitrary and D=1 for tu>0 and D=1 for tu<0. This equation describes inter alia the height of a groundwater mound during gravity-driven flow in porous media (d=2, n=1) and the propagation of strong thermal waves following an intense explosion (d=3, n=5). Using general renormalization-group (RG) arguments, we show that a radially symmetric mound exists of the form u(r,t)t-(d)f(rt-(), ), where ==1/(2+nd) and and are -dependent anomalous dimensions, obeying the scaling law n(1-nd)=0. We calculate and to O(), for general d and n, using a perturbative RG scheme. In the case of groundwater spreading, our results to O(2) are in good agreement with numerical calculations, with a relative error in the anomalous dimension of about 3% when is 0.5.

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U2 - 10.1103/PhysRevA.44.6544

DO - 10.1103/PhysRevA.44.6544

M3 - Article

AN - SCOPUS:0000110307

SN - 1050-2947

VL - 44

SP - 6544

EP - 6550

JO - Physical Review A

JF - Physical Review A

IS - 10

ER -