Emily Boudreaux
6b57738330
Note for now much of the docs is LLM written. This was done to save time and focus on code development. The docs have been LOOSLEY reviewed. However, the code itself has been either fully written by hand or fully reviewed. Therefore, the docs should at the moment be seen as a loose resource rather than authoratiative (and this is on top of the general ability for docs to drift)
247 lines
11 KiB
Groff
247 lines
11 KiB
Groff
.TH "serif::operators::BarotropicHydrostaticEquilibrium" 3 "Version v0.0.1a" "SERiF" \" -*- nroff -*-
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.ad l
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.nh
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.SH NAME
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serif::operators::BarotropicHydrostaticEquilibrium \- The constraint balancing the pressure gradient, gravitational potential, and centrifugal potential\&.
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.SH SYNOPSIS
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.br
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.PP
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.PP
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\fR#include <hydrostatic_equilibrium\&.hpp>\fP
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.SS "Public Types"
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.in +1c
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.ti -1c
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.RI "using \fBTest\fP = \fBdiscretization::blocks::enthalpy::specific\fP"
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.br
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.RI "The test type is the model specific enthalpy, which is the quantity being constrained by the hydrostatic equilibrium equation\&. "
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.ti -1c
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.RI "using \fBResidualQuantity\fP = \fBdimensions::SpecificEnthalpy\fP"
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.br
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.RI "The residual quantity is the specific enthalpy, which is the difference between the model specific enthalpy and the specific enthalpy given by the gravitational and centrifugal potentials\&. "
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.ti -1c
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.RI "using \fBPotential\fP = \fBdiscretization::blocks::gravity::potential\fP"
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.br
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.RI "We alias the gravitational potential to this type for convenience\&. "
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.ti -1c
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.RI "using \fBConstant\fP = \fBdiscretization::blocks::barotropic_constant::mass_normalization\fP"
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.br
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.RI "We alias the barotropic constant to this type for convenience\&. "
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.ti -1c
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.RI "using \fBAngularVelocity\fP = \fBdiscretization::blocks::rotation::angular_velocity\fP"
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.br
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.RI "We alias the angular velocity to this type for convenience\&. "
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.ti -1c
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.RI "using \fBOperands\fP"
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.br
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.RI "The operand here is a pack of the model specific enthalpy, the gravitational potential, the barotropic constant, and the angular velocity\&. "
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.in -1c
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.SS "Public Member Functions"
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.in +1c
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.ti -1c
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.RI "\fBBarotropicHydrostaticEquilibrium\fP (const \fBRigidRotation::Vector\fP &axis={0\&.0, 0\&.0, 1\&.0}, const \fBRigidRotation::Vector\fP ¢er={})"
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.br
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.RI "Construct a barotropic hydrostatic equilibrium equation\&. "
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.ti -1c
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.RI "PointLinearization< \fBOperands\fP > \fBevaluate\fP (const EquationPoint< \fBOperands\fP > &point) const"
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.br
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.RI "Evaluate h + Phi - Psi - C and its partial derivatives at a physical point\&. "
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.ti -1c
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.RI "template<typename OperandT> int \fBadditional_order\fP (OperandT, int position_order) const"
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.br
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.RI "Return the additional quadrature order required for the operands of this equation\&. If the operand has a functional space then the additional order is 2 * position_order - functional_space_order, otherwise it is 2 * position_order\&. "
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.in -1c
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.SS "Static Public Attributes"
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.in +1c
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.ti -1c
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.RI "static constexpr std::string_view \fBname\fP = 'hydrostatic equilibrium'"
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.br
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.RI "Compile time name for the hydrostatic equilibrium equation, used for debugging and logging\&. "
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.in -1c
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.SS "Private Attributes"
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.in +1c
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.ti -1c
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.RI "RigidRotation \fBm_rotation\fP"
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.br
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.RI "The rigid rotation object used to compute the centrifugal potential and its gradient\&. This is constructed from the axis and center of rotation provided to the constructor\&. "
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.in -1c
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.SH "Detailed Description"
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.PP
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The constraint balancing the pressure gradient, gravitational potential, and centrifugal potential\&.
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.PP
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\fBTodo\fP
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.RS 4
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This may make sense to break into smaller contributions in the same way as the displacement force equation does already\&.
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.RE
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.PP
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.PP
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If you are a physicist, astronomer, or general science goober looking to modify physics in SERiF this is likely a good place to start\&. Here we lay out a simple case of how to implement an equation\&.
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.PP
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Consider the strong form of this equation, generally
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.PP
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\[ \theta = -\left(\frac{1}{\rho}\right)\nabla P - \nabla \phi + \omega^2 s
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\]
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.PP
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where $s = \sqrt{x^2 + y^2}$ and is the cylindrical radius
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.PP
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In this particular equation we specialize this for a barotrope, for a barotrope
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.PP
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\[dh = \frac{dP}{\rho}
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\] therefore \[\nabla h = \frac{1}{\rho} \nabla P
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\]
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.PP
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Then
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.PP
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\[ \theta = -\nabla h - \nabla \phi + \omega^2 s
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\] or equivalently \[\theta = \nabla h + \nabla \phi - \omega^2 s
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\]
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.PP
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Then, in the corotating frame, we can define an effective potential $\psi = \frac{1}{2}\omega^{2}\left(x^{2} + y^{2}\right)$
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.PP
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therefore
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.PP
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\[\theta = \nabla h + \nabla \phi - \nabla \psi = \nabla (h + \phi - \psi)
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\]
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.PP
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hence
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.PP
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\[h + \phi - \psi = C
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\] or \[h + \phi - \psi - C = 0
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\]
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.PP
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This is a pointwise residual equation\&. Now broadly for finite element methods we need the weak form of this equation; this system is broadly and roughly intended to reduce friction\&. Look at the above equation then investigate HydrostaticEquilibrium::evaluate where we set the residual in the return value\&. The backend system integrates the produce of these residuals and a test function over a domain\&. The goal here is that the above step is where you as a research get to stop\&.
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.PP
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Now there are a few other things to specify here\&. For one which term does this residual contribute too\&. You must decide this however there are natural choices\&. In the case of HydrostaticEquilibrium the residual is a scalar and so it contributes to the enthalpy equation\&. You must alias the residual term to a \fBTest\fP member\&.
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.PP
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In addition to enthalpy computing the residual also depends on the gravitational potential, though the residual does not contribute to the gravitational potential equation\&. You must specify this dependency by listing the gravitational potential as an operand in the \fBOperands\fP member\&.
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.PP
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In addition to the residual there are a few additional derivatives that should be implemented or explicitly set to 0, broadly these should be a field derivative for each operand and, if the term has a spatial component, a position derivative\&.
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.PP
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The implementation below shows these trivially
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.SH "Other Notes"
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.PP
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.IP "\(bu" 2
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This is a particularly simple case as we start with a scalar valued operation\&.
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.IP "\(bu" 2
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This equation does not use the \fBContributions\fP system (mostly this is because I wrote this equation first before I wrote the contribution system)\&. There is a benefit to this in so far as I think it makes it a bit more approachable initially as it is more self contained; however, it does break the pattern that other equations use\&.
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.IP "\(bu" 2
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This is very much a place where the polytropic assumption has slipped in\&. This equation will need to be reworked or replaced to move beyond polytropes\&.
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.PP
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.SH "Member Typedef Documentation"
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.PP
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::AngularVelocity\fP = \fBdiscretization::blocks::rotation::angular_velocity\fP"
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.PP
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We alias the angular velocity to this type for convenience\&.
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::Constant\fP = \fBdiscretization::blocks::barotropic_constant::mass_normalization\fP"
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.PP
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We alias the barotropic constant to this type for convenience\&.
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::Operands\fP"
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\fBInitial value:\fP
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.nf
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utils::types::TypeList<
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discretization::forms::Operand<Test>,
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discretization::forms::Operand<Potential>,
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discretization::forms::Operand<Constant>,
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discretization::forms::Operand<AngularVelocity>
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>
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.PP
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.fi
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.PP
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The operand here is a pack of the model specific enthalpy, the gravitational potential, the barotropic constant, and the angular velocity\&. Think of this as saying that the residual for this equation depends on all of the things in this type list\&.
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::Potential\fP = \fBdiscretization::blocks::gravity::potential\fP"
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.PP
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We alias the gravitational potential to this type for convenience\&.
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::ResidualQuantity\fP = \fBdimensions::SpecificEnthalpy\fP"
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.PP
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The residual quantity is the specific enthalpy, which is the difference between the model specific enthalpy and the specific enthalpy given by the gravitational and centrifugal potentials\&.
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.SS "using \fBserif::equations::BarotropicHydrostaticEquilibrium::Test\fP = \fBdiscretization::blocks::enthalpy::specific\fP"
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.PP
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The test type is the model specific enthalpy, which is the quantity being constrained by the hydrostatic equilibrium equation\&.
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.SH "Constructor & Destructor Documentation"
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.PP
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.SS "serif::equations::BarotropicHydrostaticEquilibrium::BarotropicHydrostaticEquilibrium (const \fBRigidRotation::Vector\fP & axis = \fR{0\&.0, 0\&.0, 1\&.0}\fP, const \fBRigidRotation::Vector\fP & center = \fR{}\fP)\fR [inline]\fP, \fR [explicit]\fP"
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.PP
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Construct a barotropic hydrostatic equilibrium equation\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIaxis\fP The axis of rotation for the centrifugal potential\&. This is a vector in physical space\&.
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.br
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\fIcenter\fP The center of rotation for the centrifugal potential\&. This is a vector in physical space\&.
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.RE
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.PP
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\fBTodo\fP
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.RS 4
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Currently there is nothing constraining this axis or position to agree with the axis and center or rotation set in the force equation\&. The defaults are the same; however, we should introduce some system to ensure that these agree and that if they dont agree an error is thrown (since I cannot imagine any world in which a reasonable model would have these disagree)\&.
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.RE
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.PP
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.SH "Member Function Documentation"
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.PP
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.SS "template<typename OperandT> int serif::equations::BarotropicHydrostaticEquilibrium::additional_order (OperandT , int position_order) const\fR [inline]\fP, \fR [nodiscard]\fP"
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.PP
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Return the additional quadrature order required for the operands of this equation\&. If the operand has a functional space then the additional order is 2 * position_order - functional_space_order, otherwise it is 2 * position_order\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIoperand\fP The operand type for which to determine the additional quadrature order\&.
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.br
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\fIposition_order\fP The order of the position basis functions\&.
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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The additional quadrature order required for the given operand type\&.
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.RE
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.PP
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.SS "PointLinearization< \fBOperands\fP > serif::equations::BarotropicHydrostaticEquilibrium::evaluate (const EquationPoint< \fBOperands\fP > & point) const\fR [inline]\fP, \fR [nodiscard]\fP"
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.PP
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Evaluate h + Phi - Psi - C and its partial derivatives at a physical point\&.
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.SH "Member Data Documentation"
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.PP
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.SS "RigidRotation serif::equations::BarotropicHydrostaticEquilibrium::m_rotation\fR [private]\fP"
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.PP
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The rigid rotation object used to compute the centrifugal potential and its gradient\&. This is constructed from the axis and center of rotation provided to the constructor\&.
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.SS "std::string_view serif::equations::BarotropicHydrostaticEquilibrium::name = 'hydrostatic equilibrium'\fR [static]\fP, \fR [constexpr]\fP"
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.PP
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Compile time name for the hydrostatic equilibrium equation, used for debugging and logging\&.
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.SH "Author"
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.PP
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Generated automatically by Doxygen for SERiF from the source code\&.
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