Study of a parallel algorithm in liquid front propagation for Ceará’s soils using the finite difference method

Abstract

This work presents a numerical model to simulate the propagation of a liquid front in unsaturated soils. The governing flow equations were discretized using centered finite differences for the space coordinate and backward differences for the time coordinate. The generated scheme is fully implicit, but “lagging the non-linearities” as referred to the determination of the soil characteristic properties as function of the hydraulic head. The soil properties, moisture content and the unsaturated hydraulic conductivity, were curve fitted for two types of soil (Alluvial Eutrophic and Red-Yellow Podsol) found in the Northeast region of Brazil. The results show that the Alluvial Eutrophic liquid front diffuses faster than the Red-Yellow Podsol front. The use of a parallel algorithm showed that it can be indicated for bigger problems (2-D), where the processing speed gain can reach values between 2-3 times, against simple problems (1-D).