Class to set RHS for N-module RLC circuit with discharging capacitor, resistance, and inductance, out of each module. More...

#include <submodule_rlc_with_load_rhs.h>

Inheritance diagram for wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS:

Detailed Description

Class to set RHS for N-module RLC circuit with discharging capacitor, resistance, and inductance, out of each module.

This also includes a line inductance and resistance in the load branch along with a load. This circuit looks like the following: ____ ...______________________________

		I0 (right)

RN R2 R1 R_line

LN L2 L1 L_line

CN C2 C1 V_load | | | |

| |I2 (up) |I1 (up) |

| Ground

Each module can be switched on based on at different times. When the first line is on, we have the simple series RLC circuit with Vload (see series_rlc_with_load_rhs.h). When the successive modules are turned on, we have a a set of equations: 1) KCL -> I0 = sum_j=1^N Ij, where 2) Qdot_j = -Ij, Qdouble_dot = -Idot_j 3) KVL -> V_Cj - V_Rj - V_Lj - V_line - V_load = 0 4) V_Cj = Qj / Cj, V_Rj = Ij Rj = -Qjdot Rj, V_Lj = Ijdot Lj = -Qjdouble_dot Lj 5) V_line = L_Line * I0dot + R_line * I0 = L_line * sum_j=1^N Ijdot + R_line * sum_j=1^N Ij = -L_line * sum_j=1^N Qjdouble_dot - R_line * sum_j=1^N Qjdot We assume a vector [Q = [Q1, Q2, ..., QN], Qdot = [Q1dot, Q2dot ..., QNdot]] Equations 2 and 3 can be written as matrix equation: 6) [id 0] [Qdot] = [0 id] [Q ] + [0_N] (V_line + V_load) [0 L] [Qdouble_dot] [-C^-1 -R] [Qdot] [1_N] where L = diag(L1, L2, ..., LN), R = diag(R1, R2, ..., RN), C = diag(C1, C2, ..., CN) therefore C^-1 = diag(1/C1, 1/C2, ..., 1/CN) and 0_N is a vector of length N of zeros and 1_N is a vector of length N of ones. Also id is an identity matrix of size N x N. If we apply Eq. 5, we can rewrite Eq. 6 as 7) [id 0 ] [Qdot] = [0 id] [Q ] + [0_N] V_load [0 L_tot] [Qdouble_dot] [-C^-1 -R_tot] [Qdot] [1_N] where Ltot = L + L_line E, Rtot = R + R_line E, where E = an N x N matrix of all ones Inverting the left hand side matrix, Eq. 7 can be written 8) [Qdot] = [0 id] [Q ] + [0_N ] V_load [Qdouble_dot] [-Ltot^-1*C^-1 -Ltot^-1*R_tot] [Qdot] [Ltot^-1*1_N] where Ltot^-1 can be written using the Sherman-Morrison formula as: Ltot^-1_ij = L^-1_ij - LT / (Li * Lj) where L^-1 = diag(1/L1, 1/L2, ..., 1/LN) and where LT = L_line / (1 + L_line * sum_k=1^N (1/Lk)) note that another way to write LT is: 1 / LT = 1 / L_line + sum_k=1^N (1/Lk) which is what adding up parallel inductances looks like, but would be problematic for L_line = 0 So in the end, this app is used to solve dqdt = [Qdot, Qdouble_dot] = RHS as written in Eq. 8 using the time integrator

Public Member Functions
	SubmoduleRLCWithLoadRHS ()
	Constructor.

	~SubmoduleRLCWithLoadRHS () override
	Destructor.

void	setup (const WxCryptSet &wxc) override
	Setup.

const std::vector< int > &	getInputVariableIndexes (int flag) const override
	Grab input variable indices.

const std::vector< int > &	getAuxiliaryVariableIndexes (int flag) const override
	Grab auxiliary variable indices.

const std::vector< int > &	getOutputVariableIndexes (int flag) const override
	Grab output variable indices.

void	evaluate_function (const real q, const real aux, const solverVariables_t pSV, real result) const override
	Redefinition of the function evaluator.

Public Member Functions inherited from WmApplication
	WmApplication ()

virtual	~WmApplication ()=default

virtual void	setup (const WxCryptSet &wxc)

virtual const std::vector< int > &	getAuxiliaryVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const

virtual const std::vector< int > &	getCrossVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const

const std::vector< std::string > &	getBoundaryNames () const

bool	isOnBoundary (const std::string &boundaryName) const

bool	has (int flag) const

virtual real	numerical_flux (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const

virtual real	internal_flux (const real q, const real aux, const solverVariables_t *pSV, std::vector< std::vector< real > > &internalFlux) const

virtual real	source (const real q, const real aux, const elementGeometry_t pEG, real source) const

virtual void	bc_q (const real q_in, const real aux_in, const real aux_out, const solverVariables_t pFV, real *q_out) const
	Boundary Condition Application which sets the boundary condition on ghost nodes.

virtual real	bcNumericalFlux (const real q_l, const real q_r, const real aux_l, const real aux_r, const solverVariables_t pFV, real numericalFlux) const

virtual void	conserved_to_primitive (const real q, const real aux, real *w) const

virtual void	primitive_to_conserved (const real w, const real aux, real *q) const

virtual void	evaluate_function (const real q, const real aux, const solverVariables_t pSV, real result) const

virtual void	bc_q_kinetic (const real q_in, const real aux_in, const solverVariables_t pFV, real q_out) const

std::shared_ptr< std::string >	app_name ()

virtual const std::vector< int > &	getInputVariableIndexes (int flag=0) const

virtual const std::vector< int > &	getOutputVariableIndexes (int flag=0) const

Protected Attributes
std::vector< int >	_QI_idcs

std::vector< int >	_vload_idcs

std::vector< real >	_R

std::vector< real >	_L

std::vector< real >	_C

real	_L_line

real	_R_line

int	_N

std::vector< real >	_firetimes

real	_R_high

real	_R_max_multiplier

real	_transition_width

std::vector< std::vector< real > >	_L_inv

std::vector< std::vector< real > >	_R_tot

std::vector< std::vector< real > >	_C_inv

std::vector< std::vector< real > >	_LC

std::vector< std::vector< real > >	_LR

std::vector< real >	_R_time

Protected Attributes inherited from WmApplication
std::string	_app_name

WxLogStream	_debStrm

std::vector< int >	_allowedFlags

std::vector< std::string >	_onBoundaries

Additional Inherited Members
Public Types inherited from WmApplication
typedef Application_Variable	WmApplication_Variable

typedef std::map< std::string, std::string >	replaceMap_t

Static Public Attributes inherited from wxm::app_base
static std::vector< int >	empty

Protected Member Functions inherited from wxm::app_base
virtual	~app_base ()=default

Constructor & Destructor Documentation

◆ SubmoduleRLCWithLoadRHS()

wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::SubmoduleRLCWithLoadRHS ( )

Constructor.

◆ ~SubmoduleRLCWithLoadRHS()

wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::~SubmoduleRLCWithLoadRHS ( )

override

Destructor.

Member Function Documentation

◆ evaluate_function()

void wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::evaluate_function	(	const real *	q,
		const real *	aux,
		const solverVariables_t *	pSV,
		real *	result
	)		const

overridevirtual

Redefinition of the function evaluator.

Parameters

const	q - input variable
const	aux - auxiliary variable
const	pSV - solver variable structure
result	- output variable

Reimplemented from WmApplication.

◆ getAuxiliaryVariableIndexes()

const std::vector< int > & wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::getAuxiliaryVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab auxiliary variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of auxiliary variable indices

Reimplemented from WmApplication.

◆ getInputVariableIndexes()

const std::vector< int > & wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::getInputVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab input variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of input variable indices

Reimplemented from wxm::app_base.

◆ getOutputVariableIndexes()

const std::vector< int > & wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::getOutputVariableIndexes ( int flag ) const

inlineoverridevirtual

Grab output variable indices.

Parameters

int	flag - usually flag is given like flux type but usually not checked

Returns: vector of output variable indices

Reimplemented from wxm::app_base.

◆ setup()

void wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::setup ( const WxCryptSet & wxc )

overridevirtual

Setup.

Parameters

WxCryptSet object

Reimplemented from WmApplication.

Member Data Documentation

◆ _C

std::vector<real> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_C

protected

◆ _C_inv

std::vector<std::vector<real> > wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_C_inv

protected

◆ _firetimes

std::vector<real> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_firetimes

protected

◆ _L

std::vector<real> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_L

protected

◆ _L_inv

std::vector<std::vector<real> > wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_L_inv

mutableprotected

◆ _L_line

real wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_L_line

protected

◆ _LC

std::vector<std::vector<real> > wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_LC

mutableprotected

◆ _LR

std::vector<std::vector<real> > wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_LR

protected

◆ _N

int wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_N

protected

◆ _QI_idcs

std::vector<int> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_QI_idcs

protected

◆ _R

std::vector<real> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R

protected

◆ _R_high

real wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R_high

protected

◆ _R_line

real wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R_line

protected

◆ _R_max_multiplier

real wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R_max_multiplier

protected

◆ _R_time

std::vector<real> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R_time

mutableprotected

◆ _R_tot

std::vector<std::vector<real> > wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_R_tot

protected

◆ _transition_width

real wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_transition_width

protected

◆ _vload_idcs

std::vector<int> wxm::apps::functions::unique_variable::SubmoduleRLCWithLoadRHS::_vload_idcs

protected

The documentation for this class was generated from the following file:

src/apps/function_evaluators/unique_variable/submodule_rlc_with_load_rhs.h

Detailed Description

| |I2 (up) |I1 (up) |

Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ SubmoduleRLCWithLoadRHS()

◆ ~SubmoduleRLCWithLoadRHS()

Member Function Documentation

◆ evaluate_function()

◆ getAuxiliaryVariableIndexes()

◆ getInputVariableIndexes()

◆ getOutputVariableIndexes()

◆ setup()

Member Data Documentation

◆ _C

◆ _C_inv

◆ _firetimes

◆ _L

◆ _L_inv

◆ _L_line

◆ _LC

◆ _LR

◆ _N

◆ _QI_idcs

◆ _R

◆ _R_high

◆ _R_line

◆ _R_max_multiplier

◆ _R_time

◆ _R_tot

◆ _transition_width

◆ _vload_idcs