Rescaled Transport Model for Fluid Property Simulation
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Solution Overview
Problem
Existing modeling systems fail to accurately model fluid transport systems, particularly when the fluid flows slowly or not at all, due to non-smoothness and large fluctuations in advection and advection-diffusion models, leading to difficulties in solving differential equations.
Innovation Solution
The introduction of a rescaled transport model that smooths and modifies advection terms, combined with a time-dependent scaling factor, to address non-smoothness and fluctuations, enabling accurate modeling of fluid transport systems even at zero fluid flow points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If advection or advection-diffusion models are used to model fluid transport systems, then the model can handle fluid flow transport, but the model becomes non-smooth and exhibits large fluctuations when fluid flow is slow or zero, making differential equations difficult to solve
Solution Approach 1:
The patent applies parameter changes by introducing a scaling factor that transforms the advection term into a rescaled form. This scaling factor modifies the parameters of the transport equation to eliminate non-smoothness and large fluctuations that occur when fluid flow is slow or zero, thereby maintaining solution stability while preserving the model's ability to handle fluid transport.
Solution Approach 2:
The patent implements dynamics by making the scaling factor time-dependent. This allows the model to dynamically adapt to changing fluid flow conditions, automatically adjusting the scaling to maintain smoothness and stability across different flow regimes, including transition from slow to faster flow and vice versa.
2Adaptability or versatility
If standard advection models are used, then fluid transport can be modeled, but non-smoothness occurs at zero fluid flow points, causing computational difficulties
Solution Approach 1:
The patent transforms the computational problem by changing the parameter representation through the scaling factor. This parameter transformation simplifies the computational complexity at zero flow points by removing the non-smoothness that would otherwise require complex numerical handling, while still capturing the full range of fluid transport behavior.
3Measurement precision
If advection-diffusion models are applied, then transported property changes can be modeled, but large fluctuations occur near zero flow points, reducing accuracy
Solution Approach 1:
The patent improves measurement precision by changing the parameter scaling to eliminate large fluctuations. The rescaled advection term with the time-dependent scaling factor ensures smooth transitions near zero flow points, thereby improving the accuracy of transported property predictions while maintaining model smoothness throughout the simulation.
Solution Approach 2:
The dynamic scaling factor continuously adapts to the current flow conditions, ensuring that the model maintains both smoothness and accuracy across varying flow regimes. This dynamic adjustment allows the model to accurately capture transported property changes whether the flow is slow, zero, or fast, without experiencing the large fluctuations that would reduce precision.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The rescaled transport model allows for correct derivation of transported property behavior near zero fluid flow points, overcoming the limitations of previous models by ensuring smoothness and stability in calculations.
Implementation Method 1
the non-smoothness and large fluctuations in advection and advection-diffusion models
Data Source
AI summary
A method performed by at least one processing unit comprises receiving a selection of a control volume associated with a physical system; receiving selections of a time dependent potential variable for the transported property and a time dependent flow variable for the transported property; receiving at least one fluid flow equation; determining an advection process; determining a diffusion process; determining a time dependent scaling factor based on at least the advection process and the diffusion process; deriving a rescaled transport flow equation for the time dependent flow variable for the transported property by adding the advection process and the diffusion process, and by applying the time dependent scaling factor for normalization; solving a plurality of equations that include the fluid flow equation and the rescaled transport flow equation; deriving the time dependent flow variable for the transported property; and deriving the time dependent potential variable for the transported property.