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Burgers’ equation

Problem:

state.q[0,:]=(xc>0.4)*(xc<0.7)
solver.time_integrator='BEuler'
solver.dt_initial =1.0/128
solver.cfl_max =0.5
solver.cfl_desired = 0.4
mm=128



Time integrator
solver.time_integrator='Implicit'
solver.dt_initial =1./100
solver.cfl_max =6.6
solver.cfl_desired = 6.5
#solver.dt_variable=False

x = pyclaw.Dimension(‘x’,0.0,1.0,512) r=3.8

\(r\geq4\), CFL=6.5,5.5 you can not get the solution using fsolve

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Convergence analysis for advection equation

# Time integrator
solver.time_integrator='Implicit'
solver.dt_initial = 1./100
solver.cfl_max =5.1
solver.cfl_desired = 5
#solver.dt_variable=False    
mm=100
state.q[0,:]=mm*(sin(2*(xx[1:]-0.5)*np.pi)-sin(2*(xx[0:-1]-0.5)*np.pi))/(2*np.pi)
Implicit Yes
SSP104 No
DWSSP105 No