Manual added in doc/Manual and a note on how to implement the...

Manual added in doc/Manual and a note on how to implement the Saint-Venant-Exner approach in a coupled way in SLIM is also added

doc/Manual/chapters/appendices/Compound_Channel.geo

+start = 0;
+end = 10;
+
+//Create the points to draw the contour
+Point(1) = {start, 0.605, 0, 1.0};
+Point(2) = {start, -0.605, 0, 1.0};
+Point(3) = {start, 0.2, 0, 1.0};
+Point(4) = {start, 0.1492, 0, 1.0};
+Point(5) = {start, -0.1492, 0, 1.0};
+Point(6) = {start, -0.2, 0, 1.0};
+Point(7) = {end, 0.605, 0, 1.0};
+Point(8) = {end, -0.605, 0, 1.0};
+Point(9) = {end, 0.2, 0, 1.0};
+Point(10) = {end, -0.1492, 0, 1.0};
+Point(11) = {end, 0.1492, 0, 1.0};
+Point(12) = {end, -0.2, 0, 1.0};
+
+//Create the lines between the points
+Line(1) = {7, 1};
+Line(2) = {2, 8};
+Line(3) = {1, 3};
+Line(4) = {3, 4};
+Line(5) = {4, 5};
+Line(6) = {5, 6};
+Line(7) = {6, 2};
+Line(8) = {9, 7};
+Line(9) = {11, 9};
+Line(10) = {10, 11};
+Line(11) = {12, 10};
+Line(12) = {8, 12};
+Line(13) = {3, 9};
+Line(14) = {4, 11};
+Line(15) = {5, 10};
+Line(16) = {6, 12};
+
+//Defines the boundary of every surface. The elements will be generated separately on each surface
+Line Loop(17) = {13, 8, 1, 3};
+Plane Surface(18) = {17};
+Line Loop(19) = {14, 9, -13, 4};
+Plane Surface(20) = {19};
+Line Loop(21) = {15, 10, -14, 5};
+Plane Surface(22) = {21};
+Line Loop(23) = {16, 11, -15, 6};
+Plane Surface(24) = {23};
+Line Loop(25) = {2, 12, -16, 7};
+Plane Surface(26) = {25};
+
+//Defines the physical tags that will be used to impose the boundary conditions
+Physical Line("Wall") = {1, 2};
+Physical Line("In") = {3, 4, 5, 6, 7};
+Physical Line("Out") = {8, 9, 10, 11, 12};
+Physical Surface("Domain") = {18, 20, 22, 24, 26};
+
+//Other parameters
+Mesh.CharacteristicLengthFactor = 0.1;
+Mesh.Algorithm = 6;	

doc/Manual/chapters/appendices/Compound_Channel.py

+import slimPre
+import mySlim as slim
+from dgpy.scripts import slim_private
+import numpy
+
+##################
+##  Parameters  ##
+##################
+
+#File parameters
+meshfile = "CompoundChannel.msh"
+output_bath = "output/bath"		#Output folder for the bathymetry
+output_nc = "netcdf/"			#Output folder for NETcdf files
+mesh_start = 0
+mesh_end = 10
+
+#Time parameters
+dt = 1				#Time step
+tstart = 0			#Starting time for the hydrodynamics
+tend = 160		   	#End time of the simulation
+tinit = 80			#Starting time for the tracer equation
+tstab = 50			#Time at which the boundary conditions reach their final value
+export = dt
+
+#Bathymetry parameters
+b = 0.605
+bfp = 0.405
+h = 0.0752
+hfp = 0.0508
+s0 = 0.0019
+level = 0.0119
+
+#Parameters boundary conditions
+q = 0.015
+slip = 0.996
+
+#Flow parameters
+smagorinsky_coefficient = 0.4
+manning_mc = 0.010
+manning_w = 0.001
+manning_fp = 0.016
+
+#Parameters tracer
+concentrationIn = 0.0
+concentration = 0.0
+source = 1.0
+
+#Parameters sediment
+initial_bottom_concentration = 0.0
+windU = 1e-4 
+windV = 1e-4 
+rhosediment = 2650 
+porosity = 0.4
+rhosedimentbottom = rhosediment*(1.-porosity)
+d50 = 91e-6
+d90 = 0.0004
+shields = 0.0119
+diffusivity = 1e-6		  
+g = 9.81
+fluxMc = 1
+
+diffusivity_mode_constant = False
+diffusivity_mc = 1.2e-3
+diffusivity_w = 1.0e-3
+diffusivity_fp = 0.4e-3
+smagorinsky_coefficient = 0.3
+h = 0.063
+manning_mc = 0.010
+manning_w = 0.01
+manning_fp = 0.012
+q = 0.015
+level = 0.005
+
+#The functions to calculate various parameters are defined. They will be used later 
+def bathf(x,y) :
+    bathi = 0.
+    if abs(y) >= (b-bfp) :
+        bathi = h-hfp
+    elif abs (y) >= (b-bfp-hfp) :
+        bathi = h-(abs(y)-(b-bfp-hfp))
+    else :
+        bathi = h
+    return bathi+x*s0-level
+
+def calcEta(x,y) :
+    return -x*s0+level
+
+def calcUInit(x,y) :
+    return 0.
+
+def calcManning(x,y):
+    n = manning_mc
+    if abs(y) >= (b-bfp) :
+        n = manning_fp
+    elif abs (y) >= (b-bfp-hfp) :
+        n = manning_w
+    else :
+        n = manning_mc
+    return n
+
+def calcDiffusivity(x,y):
+    if abs(y) >= (b-bfp) :
+        d = diffusivity_fp
+    elif abs (y) >= (b-bfp-hfp) :
+        d = diffusivity_mc + (abs(y)-(b-bfp-hfp))/(hfp)*(diffusivity_fp-diffusivity_mc)
+    else :
+        d = diffusivity_mc
+    return d
+
+
+def calcC(x,y) :
+    c=concentration
+    return c
+
+def calcSource(x,y):
+    c = 0
+    if abs(y-0)<=(b-bfp-hfp)+0.0001 and abs(x)<0.1:
+        c=0.8*source/(0.1*(b-bfp-hfp)*2*h*1000)*700*q
+    return c
+
+def calcSed(x,y) :
+    sed = initial_bottom_concentration
+    return sed
+
+def calcQ(t0, i,dt):
+    t = t0 + i*dt
+    discharge = q
+    if t<tstab:
+        discharge = q/tstab*t
+    return discharge
+
+def calcEtaIn(t0,i,dt):
+    return calcEta(mesh_start,0)
+
+def calcEtaOut(t0,i,dt):
+    return calcEta(mesh_end,0)
+    
+
+
+#Parameters for the sediment
+factorW= 0.01
+wMax=0.0001
+u0erosion = 0.4
+u0deposition = u0erosion
+w0=10
+a1=0.000001
+n=4
+a01=0.028
+a02=0.144
+omega2=2.4538
+eros0Fact=0.245
+
+
+if not slim_private.path.exists(output_nc):
+    slim_private.makedirs(output_nc)
+
+###################
+### pre process ###
+###################
+
+
+#Create the object of type mesh
+mesh = slimPre.Mesh(meshfile)
+#Create the slimPre region
+region = slimPre.Region(mesh)
+#array of shape (n,3), n being the number of nodes in the region, with the coordinates of the mesh nodes
+xyz = region.coordinates
+
+#The x and y coordinates are stored in a NETcdf file
+slimPre.write_file(output_nc + 'coordinates.nc', region=region, time=None, data=[('x',xyz[:,0]),('y',xyz[:,1])])
+
+#######################
+### Flow parameters ###
+#######################
+
+#Initiates the vectors containing the flow parameters on the whole domain
+bath = numpy.zeros(xyz.shape[0])
+manning_vector = numpy.zeros(xyz.shape[0])
+diffusivity_vector = numpy.zeros(xyz.shape[0])
+
+#Fills the flow parameters as defined in the functions previously
+for i in range(xyz.shape[0]) :		
+    bath[i] = bathf(xyz[i,0], xyz[i,1])
+    manning_vector[i] = calcManning(xyz[i,0], xyz[i,1])
+    diffusivity_vector[i] = calcDiffusivity(xyz[i,0], xyz[i,1])
+	
+#The flow parameters are saved in NETcdf files, the standard input for SLIM simulations
+slimPre.write_file(output_nc + 'bath.nc', region=region, time=None, data=[('bath',bath)])
+slimPre.write_file(output_nc + 'manning.nc', region=region, time=None, data=[('manning',manning_vector)])
+slimPre.write_file(output_nc + 'sediment.nc', region=region, time=None, data=[('diffusivity',diffusivity_vector)])
+
+#Export a field in the netcdf format to msh format and gives the same name as the original mesh file but in the folder "output/bath"
+slimPre.netcdf_to_msh(meshfile, output_nc + "bath.nc", "bath", output_bath)		
+
+#####################
+### open boundary ###
+#####################
+
+#The object of type time which stores each time step is created
+time_vector = numpy.arange(0,tend+2*dt,dt,numpy.float64)
+time = slimPre.Time(time_vector)
+
+#The vectors that will hold the boundary conditions are set to zero
+#They have the same size as the time. There is one value for each time step                         
+etaOut = numpy.zeros_like(time_vector)
+discharge_vector = numpy.zeros_like(time_vector)
+
+#Fills the boundary conditions as defined previously
+for i in range(time_vector.shape[0]) :
+    etaOut[i] = calcEtaOut(tstart,i,dt)
+    discharge_vector[i] = calcQ(tstart,i,dt)
+	
+concentrationIn_vector=concentrationIn*numpy.ones_like(time_vector)
+concentrationOut_vector=concentration*numpy.ones_like(time_vector)
+
+#The boundary conditions are saved in two NETcdf files. One for the hydrodynamics, one for the sediments
+#The NETcdf files are applied to the time (time=time)
+slimPre.write_file(output_nc + 'boundaryIn.nc', region=None, time=time, data=[('dischargeIn', discharge_vector)])
+slimPre.write_file(output_nc + 'boundaryOut.nc', region=None, time=time, data=[('etaOut', etaOut)])
+slimPre.write_file(output_nc + 'sedimentBoundaryIn.nc', region=None, time=time, data=[('c', concentrationIn_vector)])
+slimPre.write_file(output_nc + 'sedimentBoundaryOut.nc', region=None, time=time, data=[('c', concentrationOut_vector)])
+
+#########################
+### initial condition ###
+#########################
+
+#Initiates the vectors for the initial conditions to zero
+etaInit = numpy.zeros(xyz.shape[0])
+uInit = numpy.zeros(xyz.shape[0])
+vInit = numpy.zeros(xyz.shape[0])
+cInit = numpy.zeros(xyz.shape[0])
+bottomConcentration_vector = numpy.zeros(xyz.shape[0])
+source_vector = numpy.zeros(xyz.shape[0])
+	
+#Fills the vector the way the initial conditions were previously defined 
+for i in range(xyz.shape[0]) :
+    etaInit[i] = calcEta(xyz[i,0], xyz[i,1])	
+    uInit[i] = calcUInit(xyz[i,0], xyz[i,1])
+    cInit[i] = calcC(xyz[i,0], xyz[i,1])
+    bottomConcentration_vector[i] = calcSed(xyz[i,0], xyz[i,1])
+    source_vector[i] = calcSource(xyz[i,0], xyz[i,1])
+
+windU_vector = windU*numpy.ones(xyz.shape[0])
+windV_vector = windV*numpy.ones(xyz.shape[0])    
+
+#The initial conditions are saved in two NETcdf files. One for the hydrodynamics, one for the sediments
+#The NETcdf file is now applied at the domain (region=region)
+slimPre.write_file(output_nc + 'init.nc', region=region, time=None, data=[('eta', etaInit),('u', uInit),('v', vInit)])
+slimPre.write_file(output_nc + 'sedimentInit.nc', region=region, time=None, data=[('c', cInit),('initial_bottom_concentration', bottomConcentration_vector),('source', source_vector),('windU', windU_vector),('windV', windV_vector)])
+
+###########
+### run ###
+###########
+
+#The object of time domain is created by giving it the NETcdf file containing the bathymetry
+domain = slim.Domain(meshfile,(output_nc + 'bath.nc','bath'))
+
+#The system of the shallow water equations is created and the optional terms are added
+eq = slim.ShallowWater2d(domain, "implicit",initial_time=tstart, final_time=tend, export_every_sub_time_step = False)
+eq.set_viscosity("smagorinsky",smagorinsky_coefficient)
+eq.set_dissipation("manning", coefficient=(output_nc + 'manning.nc','manning'))
+
+#The initial and boundary conditions are applied
+eq.set_initial_condition((output_nc + 'init.nc','eta'),(output_nc + 'init.nc','u'),(output_nc + 'init.nc','v'))    
+eq.set_boundary_open('In', discharge=(output_nc + 'boundaryIn.nc','dischargeIn'))
+eq.set_boundary_open('Out', sse=(output_nc + 'boundaryOut.nc','etaOut'))
+eq.set_boundary_coast('Wall', slip_factor=slip)
+
+#The system of the tracer equation is created and the optional terms are added
+eq2 = slim.ShallowWaterTracer2d(domain, "implicit",eq, name="tracer", offline = False, initial_time=tinit, final_time=tend)
+eq2.set_diffusivity("variable", variable_diffusivity=(output_nc + 'sediment.nc','diffusivity'))
+eq2.set_source((output_nc + 'sedimentInit.nc','source'))
+eq2.set_sediment((output_nc + 'sedimentInit.nc','initial_bottom_concentration'),(output_nc + 'sedimentInit.nc','windU'),(output_nc + 'sedimentInit.nc','windV'), rhosediment, porosity, d50, d90, shields, False, dt, factorW, wMax, u0erosion, u0deposition, w0, a01, a02, a1, n, omega2, eros0Fact)
+
+#The initial and boundary conditions are applied
+eq2.set_initial_condition((output_nc + 'sedimentInit.nc','c'))
+eq2.set_boundary_open('In', (output_nc + 'sedimentBoundaryIn.nc','c'))
+eq2.set_boundary_open('Out', (output_nc + 'sedimentBoundaryOut.nc','c'))
+eq2.set_boundary_coast('Wall')
+
+#Create an object of type Loop = temporal Solver
+loop = slim.Loop(maximum_time_step=dt, export_time=export)
+
+#Add the equations to solve
+loop.add_equation(eq)
+loop.add_equation(eq2)
+
+#The simulation starts
+loop.run()
+
+slimPre.exit(0)

doc/Manual/chapters/appendices/app0A.tex

+%
+% file: localoperator.tex
+% author: Victor Brena
+% description: Briefly describes properties of the local operator.
+%
+
+\chapter{Generating a mesh with GMSH}
+\label{app:app01}
+
+The .geo file used to generate the mesh of the compound channel using GMSH is presented hereunder as an example on how to use SLIM.
+
+
+\lstinputlisting[language=C, frame=none, backgroundcolor=\color{white}, commentstyle=\color{orange},keywordstyle=\color{cyan}, numberstyle=\footnotesize\color{darkgray},stringstyle=\color{purple}, , numbers=left]{chapters/appendices/Compound_Channel.geo}
+
+\chapter{Running a simulation with SLIM}
+\label{app:app02}
+
+The python script used for the compound channel is presented hereunder as an example on how to use SLIM.
+
+\lstinputlisting[language=Python, frame=none, backgroundcolor=\color{white}, commentstyle=\color{orange},keywordstyle=\color{cyan}, numberstyle=\footnotesize\color{darkgray},stringstyle=\color{purple},numbers=left ]{chapters/appendices/Compound_Channel.py}
+
+\
\ No newline at end of file

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