def linear_advection_parameter_comparation_with_error(errorType=2):
number_of_params = 8
alphas = np.linspace(-2.0, 2.0, number_of_params)
betas = np.linspace(0.0, 2.0, number_of_params)
gammas = np.linspace(4.0, 12.0, number_of_params)
lams = np.linspace(16.0, 95.0, number_of_params)
# params_list = [alphas]
params_list = [alphas, betas, gammas, lams]
# schemes = [[SCHEMES.TOPUS, 'alpha']]
schemes = [[SCHEMES.TOPUS, 'alpha'],
[SCHEMES.FSFL, 'beta'],
[SCHEMES.SDPUS_C1, 'gamma'],
[SCHEMES.EPUS, 'lambda']]
#advection velocity
a = 1
cases = [2]
ymins = [-0.1, -1.1]
ymaxs = [1.1, 1.1]
cfl = 0.9
nx = 400
v = 0.25
domx = [-1, 1]
domts = [[0.0, 0.25], [0, 0.125]]
for case_index in range(len(cases)):
case = cases[case_index]
ymin = ymins[case_index]
ymax = ymaxs[case_index]
domt = domts[case_index]
PATH = 'ERROR_param_compar_lin_ad_CASE=' + str(case) + '/'
for scheme_index in range(len(schemes)):
tools.clear()
scheme = schemes[scheme_index]
SCHEME = scheme[0]
params = params_list[scheme_index]
custom_path = str(SCHEME.__name__) + '_' + PATH
analitic_sol = lambda x, t: analitic_linear_advection(x, u_0, t, a, case = case)
ERRORS = []
for param in params:
marker = None#param_[-1]
SCHEME_LABEL = scheme[-1] + '=' + str(param)
initial_cond_func = lambda x: initial_cond_func_Linear_Advection(x, case = case)
error = solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func,\
initial_cond_func(domx[0]),\
initial_cond_func(domx[-1]),\
SCHEME, param,\
analitic_sol,\
SCHEME_LABEL, marker = marker,\
PATH = custom_path,\
equation_type = solver.Equation_types.Linear_advection,\
a = 1,\
save_step_by_step = False, clean_plot = False,\
ymin = ymin, ymax = ymax,
generateError = True,
errorType=errorType)
ERRORS.append(error)
tools.save_fig(params, ERRORS, PATH + scheme[0].__name__ + ".png",
scheme[0].__name__ + " cfl = " + str(cfl),
None, xlabel = "parâmetro " + scheme[-1],
ylabel = 'Erro')
def linear_advection_schemes_comparation():
alpha = 2.0
beta = 2.0
gamma = 12.0
lam = 95.0
params = [alpha, beta, gamma, lam]
schemes = [[SCHEMES.TOPUS, 'TOPUS alpha'],
[SCHEMES.FSFL, 'FSFL beta'],
[SCHEMES.SDPUS_C1, 'SDPUS-C1 gamma'],
[SCHEMES.EPUS, 'EPUS lambda']]
#advection velocity
a = 1
cases = [2, 3]
ymins = [-0.1, -1.1]
ymaxs = [1.1, 1.1]
cfl = 0.05
nx = 400
v = 0.25
domx = [-1, 1]
domts = [[0.0, 0.25], [0, 0.125]]
dx = (domx[-1] - domx[0]) / (nx-1)
x_axes = [domx[0] + i*dx for i in range(nx)]
save_analitic = True
for case_index in range(len(cases)):
tools.clear()
case = cases[case_index]
ymin = ymins[case_index]
ymax = ymaxs[case_index]
domt = domts[case_index]
t = domt[-1]
PATH = 'schemes_compar_lin_ad_CASE=' + str(case) + '/'
for scheme_index in range(len(schemes)):
scheme = schemes[scheme_index]
SCHEME = scheme[0]
param = params[scheme_index]
custom_path = PATH
if scheme_index == 0 and save_analitic:
time_precision = 4
time_string = "{:." + str(time_precision) + "f}"
fileName = custom_path + 'result'\
+ '_time=' + time_string.format(t)\
+ '_v=' + str(v)\
+ '_cfl=' + str(cfl) + '.png'
analitic = [analitic_linear_advection(domx[0] + i*dx, u_0, t, a, case = case)\
for i in range(nx)]
tools.save_fig(x_axes, analitic, fileName, 'analitica', 'analitica',\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = False, margin = 0.1, ymin = ymin, ymax = ymax)
marker = None#param_[-1]
SCHEME_LABEL = scheme[-1] + '=' + str(param)
initial_cond_func = lambda x: initial_cond_func_Linear_Advection(x, case = case)
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func,\
initial_cond_func(domx[0]),\
initial_cond_func(domx[-1]),\
SCHEME, param,\
None,\
SCHEME_LABEL, marker = marker,\
PATH = custom_path,\
equation_type = solver.Equation_types.Linear_advection,\
a = 1,\
save_step_by_step = False, clean_plot = False,\
ymin = ymin, ymax = ymax)
def linear_advection_parameter_comparation(folderPathSubName = "", cases = [2, 3]):
number_of_params = 3
alphas = np.linspace(-2.0, 2.0, number_of_params)
alphas = [float('%.2f' % el) for el in alphas]
betas = np.linspace(0.0, 2.0, number_of_params)
betas = [float('%.2f' % el) for el in betas]
gammas = np.linspace(4.0, 12.0, number_of_params)
gammas = [float('%.2f' % el) for el in gammas]
lams = np.linspace(16.0, 95.0, number_of_params)
lams = [float('%.2f' % el) for el in lams]
params_list = [alphas]
# params_list = [alphas, betas, gammas, lams]
schemes = [[SCHEMES.TOPUS, 'alpha']]
# schemes = [[SCHEMES.TOPUS, 'alpha'],
# [SCHEMES.FSFL, 'beta'],
# [SCHEMES.SDPUS_C1, 'gamma'],
# [SCHEMES.EPUS, 'lambda']]
#advection velocity
a = 1
ymins = [-1, -1.1]
ymaxs = [2, 1.1]
cfl = 0.9
nx = 400
v = 0.25
domx = [-1, 1]
domts = [[0.0, 0.25], [0, 0.125]]
dx = (domx[-1] - domx[0]) / (nx-1)
x_axes = [domx[0] + i*dx for i in range(nx)]
save_analitic = True
setters = ['.', '+', '3']
for case_index in range(len(cases)):
case = cases[case_index]
ymin = ymins[case_index]
ymax = ymaxs[case_index]
domt = domts[case_index]
t = domt[-1]
PATH = 'param_compar_lin_ad_CASE=' + str(case) + '/'
for scheme_index in range(len(schemes)):
tools.clear()
scheme = schemes[scheme_index]
SCHEME = scheme[0]
params = params_list[scheme_index]
setter_index = -1
for param in params:
setter_index = setter_index + 1
setter = setters[setter_index]
# param = param_[0]
marker = None#param_[-1]
SCHEME_LABEL = scheme[-1] + '=' + str(param)
initial_cond_func = lambda x: initial_cond_func_Linear_Advection(x, case = case)
# omitPlot = not (param == params[0] or param == params[-1])
custom_path = folderPathSubName + "_" + str(SCHEME.__name__) + '=' + str(param) + '_' + PATH
if save_analitic:
time_precision = 4
time_string = "{:." + str(time_precision) + "f}"
fileName = custom_path + 'result'\
+ '_time=' + time_string.format(t)\
+ '_v=' + str(v)\
+ '_cfl=' + str(cfl) + '.png'
analitic = [analitic_linear_advection(domx[0] + i*dx, u_0, t, a, case = case)\
for i in range(nx)]
tools.save_fig(x_axes, analitic, fileName, 'analitica', 'analitica',\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = False, margin = 0.1, ymin = ymin, ymax = ymax)
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func,\
initial_cond_func(domx[0]),\
initial_cond_func(domx[-1]),\
SCHEME, param,\
None,\
SCHEME_LABEL, marker = marker,\
PATH = custom_path,\
equation_type = solver.Equation_types.Linear_advection,\
a = 1,\
save_step_by_step = False, clean_plot = True,\
ymin = ymin, ymax = ymax,
traced = True)
def schemes_comparation_boundary_layer_equation_test():
tools.clear()
ymin = -0.1
ymax = 1.1
alpha = 2.0
beta = 2.0
gamma = 12.0
lam = 95.0
params = [alpha, beta, gamma, lam]
schemes = [[SCHEMES.TOPUS, 'TOPUS alpha'],
[SCHEMES.FSFL, 'FSFL beta'],
[SCHEMES.SDPUS_C1, 'SDPUS-C1 gamma'],
[SCHEMES.EPUS, 'EPUS lambda']]
domx = [0, 1]
domt = [0, 0.5]
PATH = 'camada_limite_schemes_comp_'
vs_nxs = [[1, 10], [0.1, 80], [0.01, 640]]
# vs_nxs = [[1, 10]]
save_analitic = True
for v_nx in vs_nxs:
v = v_nx[0]
if save_analitic:
time_precision = 4
time_string = "{:." + str(time_precision) + "f}"
fileName = PATH + '/' + 'result'\
+ '_time=' + time_string.format(domt[-1])\
+ '.png'
x_axes = np.linspace(domx[0], domx[-1], 640)
analitic = [analitic_boundary_layer_equation(x_axes[i], v)\
for i in range(640)]
tools.save_fig(x_axes, analitic, fileName, 'analitica', 'analitica_v=' + str(v),\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = False, margin = 0.1, ymin = ymin, ymax = ymax)
t = domt[-1]
for scheme_index in range(len(schemes)):
scheme = schemes[scheme_index]
custom_path = PATH + '/'
fileName = custom_path + 'result'\
+ '_time=' + time_string.format(t)\
+ '.png'
title = 'tempo = ' + str(t)
for v_nx in vs_nxs:
initial_cond_func = lambda x: initial_cond_func_Boundary_Layer(x)
v = v_nx[0]
param = params[scheme_index]
marker = '.'#_param[1]
SCHEME = scheme[0]
SCHEME_LABEL = 'v=' + str(v) + ' ' + scheme[-1] + '=' + str(param)
nx = v_nx[-1]
dx = (domx[-1] - domx[0]) / (nx-1)
dt = 0.01 / float(nx)
cfl = dt / dx
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func,\
initial_cond_func(domx[0]),\
1.0,\
SCHEME, param,\
None,\
SCHEME_LABEL, marker = marker,\
PATH = custom_path,\
equation_type = solver.Equation_types.Boundary_layer,\
a = 1,\
save_step_by_step = False, clean_plot = False,\
ymin = ymin, ymax = ymax,
customFileName = fileName,
customTitle = title,
outsideLegend=True)
def TRAB1_CFD_MESTRADO():
#max and minimum values for plot
ymin = -2.0
ymax = 2.0
#domain in x direction
domx = [0, 1]
#number of points in x direction
nx = 200
#spacing discretization size
dx = (domx[-1] - domx[0]) / (nx-1)
#FSFL param
beta = 0;
#TOPUS param
alpha = 2;
#domains in time
domts = [[0, 0.1], [0, 0.3], [0, 0.5]]
#Courant numbers
cfls = [0.1, 0.5, 0.9]
#viscosity numbers
vs = [0.001, 0.0005, 0.00025]
x_axes = [domx[0] + i*dx for i in range(nx)]
initial_condition = list(initial_cond_func_Burges(np.array(x_axes)))
name = 'results_TRAB1_CFD_MESTRADO/initial.png'
tools.save_fig(x_axes, initial_condition, name, 'Condicao inicial', 'Condicao inicial',\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = True, margin = 0.1, ymin = ymin, ymax = ymax)
#-----------------------EXERCISE 2-----------------------
#path to save results
PATH = 'results_TRAB1_CFD_MESTRADO/EXE2_'
#viscosity
v = 0.001
for cfl in cfls:
for domt in domts:
#seting upwind scheme, label and parameter
SCHEME = SCHEMES.FSFL
SCHEME_LABEL = 'FSFL'
param = beta
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func_Burges,\
initial_condition[0], initial_condition[-1], SCHEME, param,\
None,\
SCHEME_LABEL, marker = '.',\
PATH = PATH,\
equation_type = solver.Equation_types.Burges,\
a = 1,\
save_step_by_step = False, clean_plot = False,
ymin = ymin, ymax = ymax)
#seting upwind scheme, label and parameter
SCHEME = SCHEMES.ADBQUICKEST
SCHEME_LABEL = 'ADBQUICKEST'
param = cfl
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func_Burges,\
initial_condition[0], initial_condition[-1], SCHEME, param,\
None,\
SCHEME_LABEL, marker = None,\
PATH = PATH,\
equation_type = solver.Equation_types.Burges,\
a = 1,\
save_step_by_step = False, clean_plot = True,
ymin = ymin, ymax = ymax)
#--------------------------------------------------------
#-----------------------EXERCISE 3-----------------------
#path to save results
PATH = 'results_TRAB1_CFD_MESTRADO/EXE3_'
#Courant number
cfl = 0.5
for v in vs:
for domt in domts:
#seting upwind scheme, label and parameter
SCHEME = SCHEMES.FSFL
SCHEME_LABEL = 'FSFL'
param = beta
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func_Burges,\
initial_condition[0], initial_condition[-1], SCHEME, param,\
None,\
SCHEME_LABEL, marker = '.',\
PATH = PATH,\
equation_type = solver.Equation_types.Burges,\
a = 1,\
save_step_by_step = False, clean_plot = False,
ymin = ymin, ymax = ymax)
#seting upwind scheme, label and parameter
SCHEME = SCHEMES.ADBQUICKEST
SCHEME_LABEL = 'ADBQUICKEST'
param = cfl
solver.advection_difusion_equation_solver(nx, domx, domt, cfl, v,\
initial_cond_func_Burges,\
initial_condition[0], initial_condition[-1], SCHEME, param,\
None,\
SCHEME_LABEL, marker = None,\
PATH = PATH,\
equation_type = solver.Equation_types.Burges,\
a = 1,\
save_step_by_step = False, clean_plot = True,
ymin = ymin, ymax = ymax)
alpha = 2;
t = domt[-1]
x_axes = [domx[0] + i*dx for i in range(nx)]
save_analitic = False
if save_analitic:
analitic = [analitic_linear_advection(domx[0] + i*dx, u_0, 0, a, case = case)\
for i in range(nx)]
fileName = 'analitic_' + PATH + 'INITIAL.png'
tools.save_fig(x_axes, analitic, fileName, 'analitica', 'analitica',\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = True, margin = 0.1, ymin = ymin, ymax = ymax)
analitic = [analitic_linear_advection(domx[0] + i*dx, u_0, t, a, case = case)\
for i in range(nx)]
fileName = 'analitic_' + PATH + 'FINAL.png'
tools.save_fig(x_axes, analitic, fileName, 'analitica', 'analitica',\
marker = None,\
xlabel = 'x', ylabel = 'y',\
clean_plot = True, margin = 0.1, ymin = ymin, ymax = ymax)
for i in range(n_v):
SCHEME = SCHEMES.TOPUS