Search results
Results from the WOW.Com Content Network
This is a Poisson equation for the scalar function . If the vector field u {\displaystyle \mathbf {u} } is known, the above equation can be solved for the scalar function ϕ {\displaystyle \,\phi } and the divergence-free part of u {\displaystyle \mathbf {u} } can be extracted using the relation
The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is widely accepted by industry. The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam using the discharge coefficient.
In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early ...
For instance, the well-known Navier-Stokes equations that describe the time evolution of a fluid are prognostic equations that predict the future distribution of velocities in that fluid on the basis of current fields such as the pressure gradient.
Like the Riemann zeta function, the multiple zeta functions can be analytically continued to be meromorphic functions (see, for example, Zhao (1999)). When s 1, ..., s k are all positive integers (with s 1 > 1) these sums are often called multiple zeta values (MZVs) or Euler sums. These values can also be regarded as special values of the ...
The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point.
The residence time distribution function is therefore a Dirac delta function at . A real plug flow reactor has a residence time distribution that is a narrow pulse around the mean residence time distribution. A typical plug flow reactor could be a tube packed with some solid material (frequently a catalyst). Typically these types of reactors ...
Here two sets of prediction equations are combined into a single estimation scheme and a single set of normal equations. One set is the set of forward-prediction equations and the other is a corresponding set of backward prediction equations, relating to the backward representation of the AR model: