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The mathematical model is solved with numerical method.
All these problems usually need to be solved with numerical methods.
These models are solved with numerical techniques based on the feasible arc interior point algorithm (FAIPA) for nonlinear constrained optimization.
They must be solved with efficient numerical methods.
The liquid velocity field was solved with direct numerical simulations (DNS), and the bubble trajectory was calculated by Newtonian motion equation.
Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method.
Although the flow equations are solved with Direct Numerical Simulation using a low Mach number approximation, the resolution used in the computation is limited (∼1 mm) hence the inner structure of the flame and the chemical scales are not solved.
The second-order equations can also be rewritten as sets of first-order equations, which can be solved with the numerical methods such as the Runge-Kutta method [ 165].
In conclusion, the model is solved with straight forward numerical method.
This system can then easily be solved with a standard numerical scheme.
(14)–(16) is equivalent to the forward problem (1)–(3), and can be solved with the identical numerical technique.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com