Abstract
Determining the dynamic flow of soil water is an important part of water resource management and evaluation of agricultural production, and the high-efficiency and high-resolution simulation of soil-water dynamics has become the focus of numerical model research. In this study, a numerical model of groundwater flow, accelerated by a graphics processing unit (GPU) based on the compute unified device architecture (CUDA), is developed to investigate the efficiency and behavior of soil infiltration in three cases. Due to the advantages of the multithreaded operation of GPU programs, the model can reduce computation time 163-fold when the number of grids exceeds 250 × 250 under the same conditions, and acceleration is promoted with an increasing number of grids. To ensure the validity of the model, a reasonable maximum change in soil saturation should be used to control the change in time step to prevent model calculation instability. The developed model’s average absolute error and relative error do not exceed 0.94 and 0.31%, respectively, which are small compared with the results from HYDRUS. The GPU-accelerated infiltration model was found to simulate soil-water dynamics under hole irrigation accurately based on field-scale application (R2 > 0.9). The mass conservation analysis of two types of soil with alternating distribution shows that the model’s relative error is 1.47%, with an average absolute error of 0.00014 m. The GPU-accelerated infiltration model is, therefore, considered to be an effective tool due to its high efficiency and high resolution when solving two-dimensional water infiltration processes.
Résumé
La détermination du flux dynamique de l’eau du sol est une partie importante de la gestion des ressources en eau et de l’évaluation de la production agricole, et la simulation à haute efficacité et à haute résolution de la dynamique de l’eau du sol est au centre de la recherche en modélisation numérique. Dans cette étude, un modèle numérique d’écoulement des eaux souterraines, accéléré par un processeur graphique (GPU) basé sur l’architecture CUDA (Compute Unified Device Architecture), est développé pour étudier l’efficacité et le comportement de l’infiltration du sol dans trois cas. Grâce aux avantages du processus multi filière des programmes GPU, le temps de calcul du modèle peut être réduit de 163 fois lorsque le nombre de grilles dépasse 250 × 250 dans les mêmes conditions, et le nombre croissant de grilles est en faveur de l’accélération. Pour assurer la validité du modèle, un changement maximal raisonnable de la saturation du sol doit être utilisé pour contrôler le changement du pas de temps afin d’éviter l’instabilité du calcul du modèle. L’erreur absolue moyenne et l’erreur relative du modèle développé ne dépassent pas 0.94 et 0.31%, respectivement, ce qui est faible par rapport aux résultats d’HYDRUS. Le modèle d’infiltration accéléré par GPU s’est avéré capable de simuler avec précision la dynamique de l’eau du sol dans le cadre d’une irrigation ponctuelle, sur la base d’une application à l’échelle du champ (R2 > 0.9). L’analyse de la conservation de la masse de deux types de sols à distribution alternée montre que l’erreur relative du modèle est de 1.47%, avec une erreur absolue moyenne de 0.00014 m. Le modèle d’infiltration accéléré par GPU est donc considéré comme un outil efficace en raison de sa grande efficacité et de sa haute résolution lors de la résolution de processus d’infiltration d’eau en deux dimensions.
Resumen
La determinación del flujo dinámico del agua en el suelo es una parte importante de la gestión de los recursos hídricos y la evaluación de la producción agrícola, y la simulación de alta eficiencia y alta resolución de la dinámica del agua en el suelo se ha convertido en el centro de la investigación de modelos numéricos. En este estudio, se desarrolla un modelo numérico de flujo de agua subterránea, acelerado por una unidad de procesamiento gráfico (GPU) basada en la arquitectura de dispositivos unificados de computación (CUDA), para investigar la eficiencia y el comportamiento de la infiltración del suelo en tres casos. Gracias a las ventajas del funcionamiento de los programas multihilo de la GPU, el modelo puede reducir el tiempo de cálculo 163 veces cuando el número de cuadrículas es superior a 250 × 250 en las mismas condiciones, y la aceleración se potencia al aumentar el número de cuadrículas. Para garantizar la validez del modelo, debe utilizarse un cambio máximo razonable en la saturación del suelo para controlar el cambio en el paso de tiempo y evitar la inestabilidad del cálculo del modelo. El error absoluto medio y el error relativo del modelo desarrollado no superan el 0.94 y el 0.31%, respectivamente, que son pequeños en comparación con los resultados de HYDRUS. El modelo de infiltración acelerado por la GPU simula con precisión la dinámica del agua en el suelo bajo riego por aspersión en base a la aplicación a escala de campo (R2 > 0.9). El análisis de conservación de la masa de dos tipos de suelo con distribución alternante muestra que el error relativo del modelo es del 1.47%, con un error absoluto medio de 0.00014 m. El modelo de infiltración acelerado en la GPU se considera, por tanto, una herramienta eficaz por su alta eficiencia y alta resolución a la hora de resolver procesos bidimensionales de infiltración de agua.
摘要
确定土壤水的动态流动是水资源管理和农业生产评价的重要组成部分, 因此土壤水动态的高效和高分辨率模拟已成为数值模型研究的重点。在这项研究中, 开发了一个基于统一计算设备架构(CUDA)的图形处理器(GPU)加速的地下水流数值模型, 以研究三种情景下土壤入渗的效率和行为。由于GPU程序的多线程操作优势, 该模型在相同条件下当网格数超过250 × 250时, 可以将计算时间减少163倍, 并且随着网格数的增加, 加速性能提升。为保证模型的有效性, 应采用合理的最大土壤饱和度变化来控制时间步长的变化, 防止模型计算的不稳定性。所开发模型的平均绝对误差和相对误差分别不超过 0.94 和 0.31%, 与 HYDRUS 的结果相比较小。基于田间尺度应用(R2 > 0.9)表明GPU加速入渗模型可以准确模拟孔灌下的土壤水动力学过程。两种交替分布的土壤质量守恒分析表明, 该模型的相对误差为1.47%, 平均绝对误差为0.00014 m。因此, 因为其在求解二维水入渗过程中的高效率性和高分辨率, GPU 加速的入渗模型可作为一种有效的工具。
Resumo
A determinação do fluxo dinâmico da água do solo é uma parte importante da gestão dos recursos hídricos e da avaliação da produção agrícola, e a simulação de alta eficiência e alta resolução da dinâmica da água do solo tornou-se o foco da pesquisa de modelos numéricos. Neste estudo, um modelo numérico de escoamento subterrâneo, acelerado por uma unidade de processamento gráfico (UPG) baseado na arquitetura de dispositivo unificado computacional (ADUC), é desenvolvido para investigar a eficiência e o comportamento da infiltração no solo em três casos. Devido às vantagens da operação de multisegmentação de programas de UPG, o modelo pode reduzir o tempo de computação em 163 vezes quando o número de grades excede 250 × 250 nas mesmas condições, e a aceleração é promovida com um número crescente de grades. Para garantir a validade do modelo, uma mudança máxima razoável na saturação do solo deve ser usada para controlar a mudança no intervalo de tempo para evitar a instabilidade do cálculo do modelo. O erro absoluto médio e o erro relativo do modelo desenvolvido não excedem 0.94 e 0.31%, respectivamente, que são pequenos em comparação com os resultados do HYDRUS. O modelo de infiltração acelerada por UPG foi encontrado para simular a dinâmica da água no solo sob irrigação por poço com base na aplicação em escala de campo (R2 > 0.9). A análise de conservação de massa de dois tipos de solo com distribuição alternada mostra que o erro relativo do modelo é 1.47%, com um erro absoluto médio de 0.00014 m. O modelo de infiltração acelerada por UPG é, portanto, considerado uma ferramenta eficaz devido a sua alta eficiência e alta resolução na solução de processos bidimensionais de infiltração de água.
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Funding
This work is partly supported by the National Natural Science Foundation of China (No. 52079106); National Natural Science Foundation of China [Grant No. 52009104]; National Key Research and Development Program of China (No. 2016YFC0402704) and Visiting Researcher Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science (No. 2016HLG01).
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Hou, J., Pan, Z., Tong, Y. et al. High-efficiency and high-resolution numerical modeling for two-dimensional infiltration processes, accelerated by a graphics processing unit. Hydrogeol J 30, 637–651 (2022). https://doi.org/10.1007/s10040-021-02444-7
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DOI: https://doi.org/10.1007/s10040-021-02444-7