The Swedish Meteorological and Hydrological Institute projects that Sweden will experience significant climate change, with temperatures increasing by 3-5°C by 2080. This temperature rise is anticipated to bring significant changes in precipitation patterns, particularly an increase in autumn, winter, and spring rainfall, which will in turn elevate runoff volumes and rates. These shifts necessitate an improvement of stormwater management practices, particularly in urban environments where ongoing trends in urbanization, combined with the increased frequency of short-term extreme rainfall events, are likely to cause an increase in the number of flood events. Managing stormwater effectively in urban areas is crucial to achieving sustainable city objectives. One innovative approach for managing stormwater is the concept of dynamic storage in sponge-like porous bodies (SPBs). The SPB solution could be integrated with existing methods; from pipes to green roofs and small-scale infiltration practices to enhance stormwater retention. The primary research focus is on developing a theoretical model to evaluate the performance of SPBs under different conditions.

In the first paper, a pre-existing model for water uptake in a SPB up-flow storage device is further developed by refining its analysis of water absorption from impermeable to partially permeable surfaces, including scenarios involving water uptake from the saturated soil and the surrounding flood. The research investigates various conditions, such as the impact of having an impervious bottom surface with or without precipitation and examining the effects of permeable substrate under similar circumstances. A mathematical model is derived using mass conservation, Darcy’s law, and a sharp wetting front modelling approach. Results for water uptake height, flood depth, and wetting front are numerically computed and analytically resolved, where possible, with critical values identified. Parametric studies reveal increased water absorption with soil infiltration when precipitation is included, as compared to when there are no precipitation events. The model is optimized for various rainfall and soil permeability values based on Swedish rainfall data.

The second paper explores the added mass phenomenon during the initial stages of capillary flow. This understanding is important, as it improves the accuracy of modelling water absorption by porous materials governed by capillary flow, particularly in the context of SPBs. A novel approach is proposed for determining the added mass coefficient, also applicable to general scenarios involving capillary rise. Traditionally, added mass is calculated by analysing changes in kinetic energy, typically using a hemispherical cap control volume situated beneath the entrance of the tube, where the velocity profile is considered radial outside the cap and uniform within it. The added mass coefficient is computed by assuming potential flow downstream the entrance to the tube for three distinct scenarios. In the first scenario, involving the immersion of a cylindrical tube into an infinite water reservoir, the exact value of the coefficient is determined to be ​  . For the subsequent cases, which involve coaxial cylindrical structures with finite reservoir depth, both analytical derivations and numerical plots of the coefficients are presented.

The third paper revisits the first study and enhances it by incorporating the nonlinear Richards equation to account for water flow into unsaturated soils. This modification makes the model significantly more realistic by simulating water movement under various external conditions. The theoretical analysis explores the absorption process and the head pressure change. The first phase involves absorption by the soil alone, occurring when the pressure is lower than the capillary head pressure -h_c. In the second phase, both the soil and the SPB contribute to absorption within the pressure range [-h_c,0]. When full saturation is achieved, the flood is starting to form on the surface. The initial phase permits a comprehensive analytical solution, while the subsequent phase requires a blend of semi-analytical approach and numerical computations. Solutions are plotted, and the efficiency is evaluated by comparing flood formation times in the presence and absence of the SPB. Future research will focus on experimental validation of SPBs as well as further theoretical improvements to assess and enhance their effectiveness in stormwater management in urban environments affected by climate change.

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy’s law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard’s equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect.

This paper extends a previously published up-flow model for the water uptake of stormwater in sponge-like porous bodies (SPBs). The model, situated atop rain-infiltrated soil, is governed by mass conservation and Darcy’s law. Unlike in the previous study that assumed completely saturated soil, this work introduces unsaturated soil conditions using the nonlinear Richards equation, significantly increasing the model's complexity. The analysis examines the absorption process and head pressure dynamics, with two distinct phases being: the initial absorption solely by the soil and joint absorption by both soil and the SPB model until full saturation is reached. A comprehensive mathematical model is presented with an analytical solution for the initial phase, aiming to assess SPB efficiency by comparing flood formation times with and without the presence of the model.

Capillary rise dynamics play a significant role in various natural and industrial contexts. In the initial phases of capillary rise, upon immersing the cylindrical tube into an infinite water reservoir, inertial forces dominate although the length scales are normally small. Recent analytical models of capillary rise have considered these inertial effects and further resolved the problem of singularity by incorporating the added mass term. A common approach of determining added mass is by computing the change in kinetic energy, typically taking a hemispherical cap control volume below the tube entrance. Additionally, the velocity profile is assumed to be radial outside of the cap and uniform within it resulting in a sudden change of velocity. This study presents a novel approach to determining the added mass coefficient value by assuming potential flow below downstream the entrance to the tube and thus eliminating a discontinuity in the velocity profile appearing in previous solutions. Initially, a generalized model comprising a coaxial cylindrical structure is examined, and subsequently, the coefficient is derived for three specific cases. In the first case scenario, involving an immersion of a cylindrical tube into an infinite water reservoir, a more precise value of the added mass coefficient is determined to be  0.849. In the subsequent cases, involving coaxial cylindrical structure and finite reservoir depth, analytical derivations and numerical plots of the coefficients are provided.