Model Equation
To illustrate the method, consider the following one-dimensional linear wave equation
which describes a wave propagating in the -direction with a velocity . This equation is also a mathematical model for one-dimensional linear advection. Consider a typical grid point in the domain. In a one-dimensional domain, there are only two directions associated with point - left and right. If is positive the left side is called upwind side and right side is the downwind side. Similarly, if is negative the left side is called downwind side and right side is the upwind side. If the finite difference scheme for the spatial derivative, contains more points in the upwind side, the scheme is called an upwind-biased or simply an upwind scheme.
Read more about this topic: Upwind Scheme
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