0.0.1 Viscous Burger's Equation

ν=0.0015;
TMax=0.1;
uSol[x_,t_]=u[x,t]/.NDSolve[
{
(∂_t)u[x,t]+u[x,t](∂_x)u[x,t]== ν (∂_(x,x))u[x,t],
u[0,t]==0,
u[1,t]==0,
u[x,0]==Sin[2 π x]
},
u[x,t],
{x,0,1},
{t, 0, TMax}][[1]]
Plot3D[uSol[x,t],{x,0,1},{t,0,TMax},
PlotRange->All,
AxesLabel->{"x","t"}]
ContourPlot[uSol[x,t],{x,0,1},{t,0,TMax},
PlotRange->All,
AxesLabel->{"x","t"}]

0.0.2 Inviscid Burger's Equation

TMax=0.1;
uSol[x_,t_]=u[x,t]/.NDSolve[
{
(∂_t)u[x,t]+u[x,t](∂_x)u[x,t]== 0,
u[0,t]==0,
u[1,t]==0,
u[x,0]==Sin[2 π x]
},
u[x,t],
{x,0,1},
{t, 0, TMax}][[1]]
Plot3D[uSol[x,t],{x,0,1},{t,0,TMax},
PlotRange->All,
AxesLabel->{"x","t"}]
ContourPlot[uSol[x,t],{x,0,1},{t,0,TMax},
PlotRange->All,
AxesLabel->{"x","t"}]