基于Richards方程切换的土壤水流及溶质运移数值模拟
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摘要
根据每个节点的土壤水分状态来选择合适的Richards方程形式,并用隐式迭代算法求解,得到一种用于模拟土壤水盐运移过程的通用方程切换方法。该方法能自由切换任意节点的控制方程,从而充分利用水头型和含水量型Richards方程的优势,适用于所有主流的迭代求解算法。成功将该方法应用于非均质土壤饱和-非饱和的溶质运移过程模拟。通过室内及数值试验,证明其在干燥砂土淋盐及干湿交替上边界的土壤积盐等普遍难题中,相比传统数值算法能大幅度提高计算效率和精度。本文方法对大区域饱和-非饱和水流运动及溶质运移数值模拟具有显著优势及应用前景。
The high non-linearity in the hydraulic retention curve introduces potential numerical instability and mass balance error in the traditional unsaturated-saturated flow models, which subsequently increases the difficulty for solute transport simulation. This paper proposed a generalized equation switching scheme,which implicitly solves different governing equations at adjacent vertices. The proposed method is applicableto all kinds of iterative solvers and fully considers the priorities in different forms of Richards' Equation.We successfully implemented the method into a one-dimensional unsaturated-saturated flow and solute transport model. A series of soil column experiments as well as numerical tests are conducted to validate theproposed model. Regarding the difficulties in simulating(1) the salt leaching process within a dry-sandysoil column,and(2) the salt accumulation in layered soils under rapidly drying-wetting atmospheric bound-ary, the proposed model shows significant improvement in numerical accuracy and computational cost compared with the conventional HYDRUS-1 D model. The developed method is promising for the application tolarge-scale simulation of flow and solute transport.
The high non-linearity in the hydraulic retention curve introduces potential numerical instability and mass balance error in the traditional unsaturated-saturated flow models, which subsequently increases the difficulty for solute transport simulation. This paper proposed a generalized equation switching scheme,which implicitly solves different governing equations at adjacent vertices. The proposed method is applicableto all kinds of iterative solvers and fully considers the priorities in different forms of Richards' Equation.We successfully implemented the method into a one-dimensional unsaturated-saturated flow and solute transport model. A series of soil column experiments as well as numerical tests are conducted to validate theproposed model. Regarding the difficulties in simulating(1) the salt leaching process within a dry-sandysoil column,and(2) the salt accumulation in layered soils under rapidly drying-wetting atmospheric bound-ary, the proposed model shows significant improvement in numerical accuracy and computational cost compared with the conventional HYDRUS-1 D model. The developed method is promising for the application tolarge-scale simulation of flow and solute transport.
引文
[1]RICHARDS L A.Capillary conduction of liquids through porous mediums[J].Journal of Applied Physics,1931,1(5):318-333.
[2]查元源.饱和-非饱和水流运动高效数值算法研究及应用[D].武汉:武汉大学,2014.
[3]Van GENUCHTEN M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892.
[4]FARTHING M W,OGDEN F L.Numerical solution of richards’equation:A review of advances and challenges[J].Soil Science Society of America Journal,2017,81(6):1257.
[5]陈福来,任理.有限差分异质多尺度方法求解非饱和土壤水流问题的计算效率(Ⅰ):数值方法[J].水利学报,2010,41(6):640-645.
[6]张在勇,王文科,陈立,等.非饱和带有限分析数值模拟的误差分析[J].水科学进展,2016(1):70-80.
[7]查元源,朱焱,杨金忠.基于改进积分型Richards方程的区域地下水饱和-非饱和水流耦合模型[J].四川大学学报(工程科学版),2013,45(1):107-115.
[8]RATHFELDER K,ABRIOLA L M.Mass conservative numerical solutions of the head-based Richards equation[J].Water Resources Research,1994,30(9):2579-2586.
[9]吴梦喜.饱和-非饱和土中渗流Richards方程有限元算法[J].水利学报,2009,40(10):1274-1279.
[10]CELIA M A,BOULOUTAS E T,ZARBA R L.A general mass-conservative numerical solution for the unsaturated flow equation[J].Water Resources Research,1990,26(7):1483-1496.
[11]毛晓敏,尚松浩.计算层状土稳定入渗率的饱和层最小通量法[J].水利学报,2010,41(7):810-817.
[12]王少丽,许迪,方树星,等.水管理策略对土壤水盐动态和区域地下排水影响的模拟评价[J].水利学报,2005,36(7):799-805.
[13]ZHA Y,YANG J,SHI L,et al.Simulating one-dimensional unsaturated flow in heterogeneous soils with water content-based Richards equation[J].Vadose Zone Journal,2013,12(2):13.
[14]FORSYTH P A,WU Y S,PRUESS K.Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media[J].Advances in Water Resources,1995,18(1):25-38.
[15]KRABBENH?FT K.An alternative to primary variable switching in saturated-unsaturated flow computations[J].Advances in Water Resources,2007,30(3):483-492.
[16]PANICONI C,PUTTI M.A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems[J].Water Resources Research,1994,30(12):3357-3374.
[17]BROOKS R H,COREY A T.Hydraulic properties of porous media and their relation to drainage design[J].Transactions of the ASAE,1964,7(1):26-28.
[18]?IM?NEK J,SEJNA M,SAITO H,et al.The HYDRUS-1D software package for simulating the one-dimensional movement of water,heat,and multiple solutes in variably-saturated media[R].Riverside,California,2009.
[19]ABEELE W V.Hydraulic testing of crushed Bandelier Tuff[R].United States,1984.
[20]SELIM H M,SCHULIN R,FLüHLER H.Transport and ion exchange of calcium and magnesium in an aggregated soil1[J].Soil Science Society of America Journal,1987,51(4):876.
[21]LAI S,JURINAK J J.The transport of cations in soil columns at different pore velocities[J].Soil Science of America Journal,1972,36(5):730-733.
[22]MILLER C T,WILLIAMS G A,KELLEY C T.Robust solution of Richards’equation for non-uniform porous media[J].Water Resources Research,1998,34(10):2599-2610.
[23]HILLS R G,PORRO I,HUDSON D B.Modeling one-dimensional infiltration into very dry soils:1.Model development and evaluation[J].Water Resources Research,1989,25(6):1259-1269.
[2]查元源.饱和-非饱和水流运动高效数值算法研究及应用[D].武汉:武汉大学,2014.
[3]Van GENUCHTEN M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892.
[4]FARTHING M W,OGDEN F L.Numerical solution of richards’equation:A review of advances and challenges[J].Soil Science Society of America Journal,2017,81(6):1257.
[5]陈福来,任理.有限差分异质多尺度方法求解非饱和土壤水流问题的计算效率(Ⅰ):数值方法[J].水利学报,2010,41(6):640-645.
[6]张在勇,王文科,陈立,等.非饱和带有限分析数值模拟的误差分析[J].水科学进展,2016(1):70-80.
[7]查元源,朱焱,杨金忠.基于改进积分型Richards方程的区域地下水饱和-非饱和水流耦合模型[J].四川大学学报(工程科学版),2013,45(1):107-115.
[8]RATHFELDER K,ABRIOLA L M.Mass conservative numerical solutions of the head-based Richards equation[J].Water Resources Research,1994,30(9):2579-2586.
[9]吴梦喜.饱和-非饱和土中渗流Richards方程有限元算法[J].水利学报,2009,40(10):1274-1279.
[10]CELIA M A,BOULOUTAS E T,ZARBA R L.A general mass-conservative numerical solution for the unsaturated flow equation[J].Water Resources Research,1990,26(7):1483-1496.
[11]毛晓敏,尚松浩.计算层状土稳定入渗率的饱和层最小通量法[J].水利学报,2010,41(7):810-817.
[12]王少丽,许迪,方树星,等.水管理策略对土壤水盐动态和区域地下排水影响的模拟评价[J].水利学报,2005,36(7):799-805.
[13]ZHA Y,YANG J,SHI L,et al.Simulating one-dimensional unsaturated flow in heterogeneous soils with water content-based Richards equation[J].Vadose Zone Journal,2013,12(2):13.
[14]FORSYTH P A,WU Y S,PRUESS K.Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media[J].Advances in Water Resources,1995,18(1):25-38.
[15]KRABBENH?FT K.An alternative to primary variable switching in saturated-unsaturated flow computations[J].Advances in Water Resources,2007,30(3):483-492.
[16]PANICONI C,PUTTI M.A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems[J].Water Resources Research,1994,30(12):3357-3374.
[17]BROOKS R H,COREY A T.Hydraulic properties of porous media and their relation to drainage design[J].Transactions of the ASAE,1964,7(1):26-28.
[18]?IM?NEK J,SEJNA M,SAITO H,et al.The HYDRUS-1D software package for simulating the one-dimensional movement of water,heat,and multiple solutes in variably-saturated media[R].Riverside,California,2009.
[19]ABEELE W V.Hydraulic testing of crushed Bandelier Tuff[R].United States,1984.
[20]SELIM H M,SCHULIN R,FLüHLER H.Transport and ion exchange of calcium and magnesium in an aggregated soil1[J].Soil Science Society of America Journal,1987,51(4):876.
[21]LAI S,JURINAK J J.The transport of cations in soil columns at different pore velocities[J].Soil Science of America Journal,1972,36(5):730-733.
[22]MILLER C T,WILLIAMS G A,KELLEY C T.Robust solution of Richards’equation for non-uniform porous media[J].Water Resources Research,1998,34(10):2599-2610.
[23]HILLS R G,PORRO I,HUDSON D B.Modeling one-dimensional infiltration into very dry soils:1.Model development and evaluation[J].Water Resources Research,1989,25(6):1259-1269.