Conversion Between Different Variables
It is possible to write the Euler equations in terms of different sets of variables. The default is to use conservative variables, but there are others as well, such as entropy variables. This page describes how to convert between the different sets of variables. The functions perform conversions back and forth between conservative variables and the "other" variables. The code generally does not support conversion directly between two different sets of "other variables. For example, if we call the conservative variables the q variables, the first set of "other" variables the w1 variables and the second set of "other" variables the w2 variables, it is possible to convert between q and w1 as well as q and w2 but not between w1 and w2.
The basic set of functions perform the conversion, and these function's names and in an underscore. Layered on top of these functions are a safer method of conversion, which uses the static parameters of the ParamType to determine what variables are stored in eqn.q and performs the appropriate conversion. This is important because if, for example, we are solving the equation using entropy variables, and the function convertToEntropy is called, it will (correctly) not do the conversion, because the variables are already the entropy variables. If convertToConservative is called, it will do the proper conversion from entropy to conservative variables.
The function describe here provide one additional bit of functionality. Lets say a function needs to convert it current variables to conservative variables, do some operation, then convert the result back to entropy variables. Converting to conservative variables is easy, that's what convertToConservative does. The problem is converting back. The code doesn't necessarily know what variables are stored in eqn.q, so it doesn't know what function to call. Should it call convertToW1 or convertToW2? The solution is convertFromNaturalToWorkingVars, which converts from the conservative variables to whatever the variables stored in eqn.q are (as determined by the static parameters of the ParamType object).
Functions
EulerEquationMod.convertFromNaturlaToWorkingVars
This function converts a vector qc from the "natural" set of variables to write the equation to the set of variables the equation is being solved in, defined by the static parameter var_type of the params. For the Euler equations, the "natural" variables are the conservative variables. Every new set of variables must extend this function with a new method.
Inputs: params: ParamType{Tdim, var_type} qc: vector of "natural" variables
Inputs/Outputs: qe: vector to be populated with the new variables
Low level function.
Aliasing restrictions: none (this requires that every method of this function support in-place conversion).
EulerEquationMod.convertToConservative — Method.low level function
Converts conservative variables to conservative variables (ie. it copies the input to the output). This method exists to values can be converted without knowing whether they are conservative or entropy.
Aliasing restrictions: none (qc and qe can be the same vector)
EulerEquationMod.convertToConservative — Method.EulerEquationMod.convertToConservative
Converts the entropy variables at a node to the conservative variables.
Inputs: params : ParamType{2, :entropy} used to dispatch to the proper method qe : vector (of length 4) of entropy variables
Inputs/outputs qc : vector (of length 4) of conservative variables. Contents of vector are overwritten
Aliasing: none (qc and qe can be the same vector)
Ths is a low level function.
EulerEquationMod.convertToConservative — Method.mid level function
Converts the array (3D form) of entropy variables to conservative variables in place. If the array is already in conservative variables this is a no-op. Other methods exist if q_arr is a vector.
Inputs: mesh sbp eqn opts
Inputs/Outputs: q_arr: array of values (3D) to be converted
Aliasing: no restrictions
EulerEquationMod.convertToConservativeFromIR_
Converts the IR entropy variables at a node to the conservative variables regardless of the static parameter var_type.
Inputs: params : ParamType{Tdim} used to dispatch to the proper method qe : vector (of length 4 or 5) of entropy variables
Inputs/outputs qc : vector (of length 4 or 5) of conservative variables. Contents of vector are overwritten
Aliasing: none (qc and qe can be the same vector)
Ths is a low level function.
EulerEquationMod.convertToConservative_ — Method.EulerEquationMod.convertToConservative_
Converts the entropy variables at a node to the conservative variables regardless of the static parameter var_type.
Inputs: params : ParamType{Tdim} used to dispatch to the proper method qe : vector (of length 4 or 5) of entropy variables
Inputs/outputs qc : vector (of length 4 or 5) of conservative variables. Contents of vector are overwritten
Aliasing: none (qc and qe can be the same vector)
Ths is a low level function.
EulerEquationMod.convertToEntropy — Method.EulerEquationMod.convertToEntropy
Converts the conservative variables at a node to entropy variables
Input: params : ParamType{s, :conservative} qc : vector (of length 4 or 5) of conservative variables
Outputs: qe : vector (of length 4 or 5) of conservative variables. Contents of vector areoverwritten
low level function
Aliasing restrictions: none (qc and qe can be the same vector)
EulerEquationMod.convertToEntropy — Method.EulerEquationMod.convertToEntropy
Converts the entropy variables to entropy variables (ie. it copies the input to the output). This method exists so variables can be converted to entropy variables without knowing what type they are.
low level function
Aliasing restrictions: none (qc and qe can be the same vector)
EulerEquationMod.convertToEntropy — Method.mid level function
Converts the array (3D form) of conservative variables to entropy variables in place. If the array is already in entropy variables this is a no-op
Methods also exist for the 1D form.
Inputs: mesh sbp eqn opts
Inputs/Outputs: q_arr: array of values (3D) to be converted
Aliasing: no restrictions
EulerEquationMod.convertToEntropy_ — Method.EulerEquationMod.convertToEntropy_
Converts the conservative variables at a node to the entropy variables regardless of the static parameter var_type.
Inputs: params : ParamType{Tdim} used to dispatch to the proper method qe : vector (of length 4 or 5) of conservative variables
Inputs/outputs qc : vector (of length 4 or 5) of entropy variables. Contents of vector are overwritten
Aliasing: none (qc and qe can be the same vector)
Ths is a low level function.
EulerEquationMod.convertToIR_ — Method.EulerEquationMod.convertToIR_
Converts the conservative variables at a node to the entropy variables of Ismail and Roe regardless of the static parameter var_type.
Inputs: params : ParamType{Tdim} used to dispatch to the proper method qe : vector (of length 4 or 5) of conservative variables
Inputs/outputs qc : vector (of length 4 or 5) of entropy variables. Contents of vector are overwritten
Aliasing: none (qc and qe can be the same vector)
Ths is a low level function.