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Kinematic wave equations are solved with a nonlinear scheme using Newton's method, from upstream to downstream cells (the order of execution is important). For multi-threading and GPU support (#541) work (with a focus on local inertial routing), the finite difference representation for flow $q$ for the $n\text{th}$ cell at time $k$ used by the Grid-to-Grid model routing scheme is an interesting option:
where $\theta = c \Delta{t}/\Delta{x}$ is the dimensionless wave speed ($c$ is the wave speed) and $u$ is total lateral inflow per unit length. For this formulation the order of execution is not important as the flow from cell $n$ at time $k$ depends on upstream inflow at the previous time ($q^{n-1}_{k-1}$) and flow from cell $n$ at the previous time ($q^n_{k-1}$).
The text was updated successfully, but these errors were encountered:
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May 20, 2025
Kinematic wave equations are solved with a nonlinear scheme using Newton's method, from upstream to downstream cells (the order of execution is important). For multi-threading and GPU support (#541) work (with a focus on local inertial routing), the finite difference representation for flow$q$ for the $n\text{th}$ cell at time $k$ used by the Grid-to-Grid model routing scheme is an interesting option:
where$\theta = c \Delta{t}/\Delta{x}$ is the dimensionless wave speed ($c$ is the wave speed) and $u$ is total lateral inflow per unit length. For this formulation the order of execution is not important as the flow from cell $n$ at time $k$ depends on upstream inflow at the previous time ($q^{n-1}_{k-1}$ ) and flow from cell $n$ at the previous time ($q^n_{k-1}$ ).
The text was updated successfully, but these errors were encountered: