There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/329/lectures/node89.html

But I haven't seen anyone propose and "implicit" upwin scheme like this: $\frac{T^{n+1}_i-T^{n}_i}{\tau}+u\frac{T^{n+1}_i-T^{n+1}_{i-1}}{h_x}=0$.

All the upwind schemes I've seen were dealing with data on the previous time-step in the spacial derivative. What is the reason for that? How does the classical upwind scheme compare to the one I wrote above?

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/329/lectures/node89.html

But I haven't seen anyone propose an "implicit" upwind scheme like this: $\frac{T^{n+1}_i-T^{n}_i}{\tau}+u\frac{T^{n+1}_i-T^{n+1}_{i-1}}{h_x}=0$.

All the upwind schemes I've seen were dealing with data on the previous time-step in the spacial derivative. What is the reason for that? How does the classical upwind scheme compare to the one I wrote above?