Conceptual Modelling Flashcards
Focussing on the ASSUME and GIVEN sections
What is a conceptual model?
A reduced representation of the complex system under study. It includes a brief summary of the relevant physics, domain, ICS, BCs, and model parameters.
What types of equations are required when defining the key physics? What questions should you ask yourself?
Two types of equations (one conservation equation required - mass, momentum, energy). What physics will you need to replicate the key observations? What physics will you need to predict the key outcomes?
Define ‘the domain’ of a model.
The domain is where in time and space (the independent variables) the model is valid. There is usually a somewhat optimal solution - needs to be large enough to capture the processes of interest.
What are boundary and initial conditions?
A consequence of selecting the model domain. They can be parameters.
What is required when conducting a literature review?
Before beginning model development, look at model approaches that have/haven’t worked and their pros and cons. Look at any available data applicable to the model, different applications could still be useful for validation. Look for probable parameter values (material parameters, BCs, ICs).
- What worked in the past
- past data
- possible physics/parameter/BCs,ICs
What is the simplified model notation?
y = f(x, theta)
y is the output of the model (dependent variable)
x is the vector of inputs (independent variable e.g time, space)
theta is the vector of parameters
f(.) is the operator that converts inputs into outputs (e.g python function euler method)
What are parameters?
Parameters are terms within the governing equations that remain constant when put through the mathematical model.
What are the four types of parameters in mathematical models?
Constants (gravity), known but situation dependent (mass of story of building), uncertain but have a range (stiffness), unknown (damping coefficient).
What is one thing to be wary of when determining parameters of models?
Ensure that the parameter does not vary with the dependent variable (not actually a parameter). Either create a model with its own parameters to model the change or assume an appropriate constant value.
What is the difference between a simulator and a model?
A simulator is a computer program that accepts parameters, BCs, ICS, geometry, and applies the appropriate physical evolution to produce an output.
A model is an abstract or numerical representation of a specific reality. It includes the parameters, BCs, ICS, geometry, as well as the simulated output.
What are black boxes?
They are a simulator or model whose internal workings are not fully understood. Input to output without full understanding.
List the key components of a conceptual model and given an example of each.
Parameters (mass), boundary conditions (volume/maximum mass of system), initial conditions (mass at time 0), domain (time and space that it is valid).
How is a conceptual model different to a computational model?
A conceptual model is a simplified representation of a complex system. It involves a concise summary of the relevant physics, parameters, ICS, BCs, and domain. A computational model is the complex system that is under study. A conceptual model is often used to develop the computational model.
How is the model domain different to a model grid?
The model domain is the where in time and space the model is valid. The model grid is the discretisation of the domain into its computational elements. It enables the application of numerical methods to solve governing equations.
What kinds of information are useful to obtain as you prepare a modelling study?
Probable parameter values, modelling approaches that did/did not work and their pros and cons, data directly relevant or not, to use in the calibration process.
