A Web Based Partial Differential Equation Solver as a General Modeling System for Environmental Problems A Web Based Partial Differential Equation Solver as a General Modeling System for Environmental Problems Environmental System Research Laboratory Dept. of Environmental Engineering Kangwon National University, Korea Joon Hyun Kim, and Young Han Han| KNU-ESRL June 2007 Introduction - Increase of importance for conservation and management of water environment water environment - Development and application of computational model for environment management for environment management : Use of analytical solution and numerical analysis technique : Use of analytical solution and numerical analysis technique : Difficulty and troublesomeness of program development for each problem : Difficulty and troublesomeness of program development for each problem - Commercial partial differential equation solver (CFD) : PHOENICS, FLUENT, ABAQUS, ANSYS, etc. : PHOENICS, FLUENT, ABAQUS, ANSYS, etc. : Mechanical, aerospace, atomic, chemical, civil engineering, etc. : Mechanical, aerospace, atomic, chemical, civil engineering, etc. : Unsuitableness to construct of main variables, parameters, and reaction : Unsuitableness to construct of main variables, parameters, and reaction mechanism of analyzed problem mechanism of analyzed problem - Need the partial differential equation solver which can easily analyze the environmental problems can easily analyze the environmental problems KNU-ESRL 1. Research Objective - Migration of fluids and pollutants : Representation into general partial differential equation based upon : Representation into general partial differential equation based upon mass, momentum, and energy equation mass, momentum, and energy equation - Development of partial differential equation analysis program using multidimensional finite element model program using multidimensional finite element model : Numerical analysis modules for each differential term : Numerical analysis modules for each differential term : Independently integrated and object oriented system : Independently integrated and object oriented system : Construction of main variables, parameters, and reaction mechanism : Construction of main variables, parameters, and reaction mechanism of analyzed problems of analyzed problems - Program can easily analyze the environmental problems : basin, surface and subsurface water, sewer, and sea : basin, surface and subsurface water, sewer, and sea - Operation on the basis of world wide web KNU-ESRL 2. Survey on Past Models Techniques of phenomena analysis KNU-ESRL General numerical analysis methods KNU-ESRL Commercial CFD program - PHOENICS, ANSYS, ABAQUS, NASTRAN, FLUENT, etc. Watershed management model - SWMM, STORM, RRL, ILLUDAS, HSPF, UCURM, etc. Surface water hydraulic model - TIDE4, HEC-2, FESWMS-2DH, RMA2, DYNHYD2, etc. Surface water quality model - MFEMWASP, QUAL2E, WASP5, WQRRS, CE-QUAL-W2, RMA-4, etc. CE-QUAL-W2, RMA-4, etc. KNU-ESRL Hydraulics and water quality model of subsurface - PM5 : MODFLOW, MOC 3D, MT3D Underground gas migration model : MFEMGAS Composite multiphase groundwater model : CMGM Sewer management model : TRANSPORT, EXTRAN Predictive control model of WWTP : ASIM, PHOENICS Waterworks management model : FEMCL KNU-ESRL Web based operation - Terminal Client Service of Window Operation on internet using ActiveX Document of MS-VB Integrated operation with GIS - Combination of GIS and computational model - Construction of image and contribute data for study area (on ArcView) (on ArcView) - Analysis of input data and modeling result of model Web-GIS using ArcExplorer, MapCafe and MapObject Web-GIS using ArcExplorer, MapCafe and MapObject of ESRI, and MS-VB of ESRI, and MS-VB KNU-ESRL 3. Development of Comprehensive Partial Differential Equation Solver(WPDES) Differential Equation Solver(WPDES) - Development of multidimensional finite element model : Minimization of numerical error and instability : Minimization of numerical error and instability : Combination of module for each differential term of PDE : Combination of module for each differential term of PDE : Analysis of boundary condition is easy : Analysis of boundary condition is easy : Easy combination with GIS using a square grid networks : Easy combination with GIS using a square grid networks : Object oriented program based on independently numerical analysis logic : Object oriented program based on independently numerical analysis logic - Integral modules to estimate the differential term(space, time) - Discretization of governing equation using integral modules - Algorithm of comprehensive PDE analysis model KNU-ESRL 3.1 Multidimensional Finite Element Modules - Discretization of main variables and parameters using basis function - Estimation of node coordinates for each elements using basis function - Construction of weighting residual eq. for the governing eq. KNU-ESRL Transformation of global coordinates into local ones coordinates into local ones KNU-ESRL Definition of element integral matrices using FEM - Integral matrix without spatial differential term - Differential term for weighting function - Differential term for main variables - Integral matrix with 2nd order differential term for main variables KNU-ESRL Analysis of boundary condition using FEM - 1st boundary condition - 2nd boundary condition 1-dim. : 2-dim. : 3-dim. : - 3rd boundary condition KNU-ESRL Rainfall runoff and pollutants migration model in basin 3.2 Application of developed method to environmental problems to environmental problems - 2-dim. runoff by rainfall - Flow in waterway KNU-ESRL Surface water hydraulic model - 1-dim. flow of surface water (continuity eq.) - 1-dim. flow of surface water (momentum eq.) KNU-ESRL - 2-dim. flow of shallow sea (continuity eq.) - 2-dim. flow of shallow sea (momentum eq.) KNU-ESRL - 2-dim. flow of lake and river (continuity eq.) - 2-dim. flow of lake and river (momentum eq.) KNU-ESRL - Assembling of continuity and momentum eq. into finite element matrix KNU-ESRL Surface water quality model - Water quality model - Thermal change model of waterbody KNU-ESRL Subsurface water hydraulics and pollutants migration model - Subsurface water hydraulic model - Pollutants migration model KNU-ESRL Multidimensional gas flow model in soil - Gas flow model in soil - Composite migration model in gas phase KNU-ESRL Composite multiphase model for NAPL analysis KNU-ESRL Sewer flow and pollution analysis model - Continuity equation - Momentum equation Waterworks management model KNU-ESRL 3.3 Modules of WPDES model - Input and output - Modules related to space domain : Basis and Weighting function : Basis and Weighting function : Estimation of nodes and coefficients for each element : Estimation of nodes and coefficients for each element - Calculation of element matrices - Assembling of element matrices - Analysis of nonlinear system - Analysis of reaction and constitution equation - Analysis of boundary condition KNU-ESRL 3.4 Example of modules in WPDES model c c********************************************** subroutine femc c********************************************** c include mfemwasp.cmn' c c... form the r.h.s global matrix [sk] and c the l.h.s load vector f... c if(node.eq.2) call asem1 if(node.eq.4) call asem2 if(node.eq.8) call asem3 c c... include boundary conditions for each system... c if(indb1(nis).eq.1) call bound1 if(node.eq.2.and.indb2(nis).eq.1) call bound12 if(node.eq.4.and.indb2(nis).eq.1) call bound22 if(node.eq.8.and.indb2(nis).eq.1) call bound32 if(node.eq.2.and.indb3(nis).eq.1) call bound13 if(node.eq.4.and.indb3(nis).eq.1) call bound23 if(node.eq.8.and.indb3(nis).eq.1) call bound33 c c... solve the system of linear equations... c c if(time.eq.dt) then call solve(1,sk,f,np,ihalfb,nis) c endif call solve(2,sk,f,np,ihalfb,nis) c c... store the solution in vector ce(i,nis)... c... reset the variable for time domain... c do ip=1,np ce(ip,nis)=f(ip,nis) if(ce(ip,nis).le.0) ce(ip,nis)=-0.6*ce(ip,nis) oldce(ip,nis)=ce(ip,nis) end do c return end Concentration calculation calculation module module KNU-ESRL c c********************************************** subroutine asem3 c********************************************** c include 'femwasp.cmn' include 'elemen.cmn' c eps=ep-1.0 c c... initialize global matrix [sk] and load vector f c c if(time.eq.dt) then do i=1,np f(i,nis)=0.d0 do j=1,iband sk(i,j,nis)=0.d0 end do c endif c c... evaluate parameters... c call reaction call source c c... begin assembling process... c do nel=1,ne c c... set local coordinates and point load in each element... c do ia=1,node ijkia=ijk(ia,nel) xe(ia)=x(ijkia) ye(ia)=y(ijkia) ze(ia)=z(ijkia) rke(ia)=rk(ijkia,nis) soure(ia)=sour(ijkia,nis) end do c c... set parameters in each element... c c... velocity... c v1x=vx(nel) v1y=vy(nel) v1z=vz(nel) c c... dispersion coefficient tensor... c d1xx=dxx(nel)*v1x d1xy=dxy(nel)*v1x d1xz=dxz(nel)*v1x d1yx=dyx(nel)*v1y Assembling module d1yy=dyy(nel)*v1y d1yz=dyz(nel)*v1y d1zx=dzx(nel)*v1z d1zy=dzy(nel)*v1z d1zz=dzz(nel)*v1z c c... compute the [et], [ev], [ed], [etk], [ets] matrix... c call element3(et,evx,evy,evz,edxx,edxy,edxz,edyx,edyy,edyz, & edzx,edzy,edzz,etk,ets,v1x,v1y,v1z,d1xx,d1xy,d1xz,d1yx,d1yy,d1yz, & d1zx,d1zy,d1zz,xe,ye,ze,rke,soure) c c... assemble [et], [ev], [ed], [etk], [ets] and form [sk]... c c if(time.eq.dt) then do i=1,node ijki=ijk(i,nel) do j=1,node ijkj=ijk(j,nel) ji=ijkj+(ihalfb+1)-ijki if(ji.le.0) goto 99 if(ji.gt.iband) goto 99 sk(ijki,ji,nis)=sk(ijki,ji,nis)+et(i,j)+ & ep*(evx(i,j)+evy(i,j)+evz(i,j)+edxx(i,j)+edxy(i,j)+edxz(i,j) & +edyx(i,j)+edyy(i,j)+edyz(i,j)+edzx(i,j)+edzy(i,j)+edzz(i,j) & -etk(i,j)) end do c endif c c... assemble [et],[ev],[ed],[etk],[ets] c and form r.h.s. vector f... c do i=1,node fe(i,nis)=0.d0 ijki=ijk(i,nel) do j=1,node ijkj=ijk(j,nel) fe(i,nis)=fe(i,nis)+(et(i,j) &+eps*(evx(i,j)+evy(i,j)+evz(i,j)+edxx(i,j)+edxy(i,j)+edxz(i,j) & +edyx(i,j)+edyy(i,j)+edyz(i,j)+edzx(i,j)+edzy(i,j)+edzz(i,j) & -etk(i,j)))*oldce(ijkj,nis)+ets(i,j) end do f(ijki,nis)=f(ijki,nis)+fe(i,nis) end do c end do goto 999 c 99 write(*,*) 'computation stop due to band width' c 999 return end KNU-ESRL 4. Verification and Application of WPDES model of WPDES model 4.1 Verification of WPDES model - Analytical solution - Comparison of 1,2,3-dim modeling results for 1-dim. problem for 1-dim. problem - Comparison with experimental data - Comparison with modeling result of another model KNU-ESRL Model verification using analytical solution - Element network used for model verification - Convective dominant transport (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) - Dispersive dominant transport (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) - Middle case (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) (Velocity V=0.369m/day, Diffusion coeff. D= m 2 /day) KNU-ESRL - Verification result using analytical solution KNU-ESRL Comparison of 1,2,3-dim modeling - Element network used for model verification KNU-ESRL - 1,2, and 3-dim. modeling result KNU-ESRL - 1,2, and 3-dim. modeling result KNU-ESRL Comparison with experimental data - Comparison result for gas migration problem KNU-ESRL - Comparison result for gas migration problem KNU-ESRL Comparison of two modeling results - Model and input data used for verification KNU-ESRL - Comparison of modeling results KNU-ESRL 4.2 Combination of WPDES and GIS Combination of ArcView and Fortran compiler KNU-ESRL Operation of WPDES model on ArcView KNU-ESRL Analysis of WPDES modeling result KNU-ESRL 4.3 Operation of Web based model Scheme of web based operation KNU-ESRL Remote access using TSC of Window 2000 KNU-ESRL Remote operation using TSC KNU-ESRL Scheme of Web-GIS operation - Web based operation of GIS in combination with WPDES - Extension of application using MapObject - Construction of GUI using MS-VB - Web based operation using ActiveX Control - Preparation of web page using ASP(Active Server Page) - Application and control using IIS(Internet Information Service) and Active Directory of Window2000 Service) and Active Directory of Window2000 KNU-ESRL Web GIS using ActiveX control KNU-ESRL Web GIS using ArcView IMS and ArcIMS KNU-ESRL Web based model operation using ASP KNU-ESRL Construction of interface using VB KNU-ESRL 4.4 Application of WPDES model Surface water environment management - Calculation of pollutant loading for each sub-baisin (Youngwol Lake) KNU-ESRL - Construction of image data (site information) KNU-ESRL - Construction of image data (non-point source) KNU-ESRL - Data construction for finite element grid network (Paldang Lake) KNU-ESRL - Analysis of input data for each element (Youngwol Lake) KNU-ESRL - Modeling result for Younwol Lake (BOD) KNU-ESRL - Modeling result for Paldang Lake (BOD) KNU-ESRL Subsurface environment managemant - Analysis of subsurface migration of TCE using WPDES KNU-ESRL - Analysis of gas migration in soil t=10min t=100min t=300min t=400min t=200min KNU-ESRL - Data construction of subsurface environmental quality KNU-ESRL - Analysis of subsurface water flow KNU-ESRL Sewer management - Data construction of sewer facilities KNU-ESRL - Analysis of sewer facilities information (slope, length, diameter, elevation) KNU-ESRL - Modeling result of sewer flow for each pipe KNU-ESRL - Modeling results of sewer water quality for each pipe KNU-ESRL Waterworks management - Prediction of chlorine behavior at disinfection process (pH=6.14, Temp. =297.5) KNU-ESRL - Prediction of chlorine behavior at disinfection process (pH=6.05, Temp. =293) KNU-ESRL 5. Conclusions - Development of multidimensional finite element modules, which is object oriented and integrated independently which is object oriented and integrated independently - Development of web based comprehensive partial differential equation solver differential equation solver - Study on stability of developed model(WPDES) - Study on applicability of WPDES for the fields of environment environment - Real-time operation scheme on the basis of web - Model operation using Web-GIS - Good applicability for various fields of environment KNU-ESRL 6. Future Works - More detailed analysis of reaction coefficients and parameters - Extension of user-friendly GUI includeing help function - Development of pre- and post-processor - Establishment of web based operating system - Proposition into more effective tool through comprehensive application concerned with various environmental problems application concerned with various environmental problems KNU-ESRL