ISOTHERMAL Euler flux in POLAR geometry (ring r, theta), 3 variables (rho, rho v_r, rho v_theta) – "polar fluid grid" effort, Path A step 1. More...

#include <hyperbolic.hpp>

Inheritance diagram for pops::IsothermalFluxPolar:

Collaboration diagram for pops::IsothermalFluxPolar:

Public Member Functions
POPS_HD StateVec< 3 >	polar_geom_source (const StateVec< 3 > &u, Real r) const

Public Member Functions inherited from pops::IsothermalFlux
POPS_HD Real	velocity_rho (Real rho) const
	rho clamped from below by vacuum_floor for the velocity division ONLY.

POPS_HD StateVec< 3 >	flux (const StateVec< 3 > &u, const Aux &, int dir) const

POPS_HD Prim	to_primitive (const StateVec< 3 > &u) const
	Conservative -> primitive: (rho, rho u, rho v) -> (rho, u, v).

POPS_HD StateVec< 3 >	to_conservative (const Prim &p) const
	Primitive -> conservative: (rho, u, v) -> (rho, rho u, rho v).

POPS_HD Real	max_wave_speed (const StateVec< 3 > &u, const Aux &, int dir) const

POPS_HD StateVec< 3 >	eigenvalues (const StateVec< 3 > &u, const Aux &, int dir) const
	Full spectrum: (v_dir - c, v_dir, v_dir + c), c = sqrt(cs2).

POPS_HD void	wave_speeds (const StateVec< 3 > &u, const Aux &, int dir, Real &smin, Real &smax) const
	Signed speeds (HLL/HLLC): v_dir -+ c_s.

Additional Inherited Members
Public Types inherited from pops::IsothermalFlux
using	State = StateVec< 3 >
	conservative variables (rho, rho u, rho v)

using	Prim = StateVec< 3 >
	primitive variables (rho, u, v)

Static Public Member Functions inherited from pops::IsothermalFlux
static VariableSet	conservative_vars ()

static VariableSet	primitive_vars ()

Public Attributes inherited from pops::IsothermalFlux
Real	cs2 = 1

Real	vacuum_floor = 0
	Quasi-vacuum density floor (ADC-77).

Static Public Attributes inherited from pops::IsothermalFlux
static constexpr int	n_vars = 3

Detailed Description

ISOTHERMAL Euler flux in POLAR geometry (ring r, theta), 3 variables (rho, rho v_r, rho v_theta) – "polar fluid grid" effort, Path A step 1.

This is a brick SEPARATE from IsothermalFlux (Cartesian): the PHYSICAL flux and the conversions are IDENTICAL (the components 1, 2 are the momentum in the LOCAL ORTHONORMAL BASIS (e_r, e_theta); dir 0 = radial, dir 1 = azimuthal), but this brick adds the GEOMETRIC CURVATURE TERM carried by the polar metric. We inherit IsothermalFlux to NOT duplicate flux / conversions / wave speeds (Cartesian strictly intact, bit-identical) and add ONLY the polar_geom_source method.

WHY AN EXPLICIT GEOMETRIC TERM (and not a plain conservative divergence): the vector momentum equation d_t(rho v) + div(rho v (x) v) + grad p = 0, projected onto the LOCAL polar basis (e_r, e_theta) which ROTATES with theta, gives for the PHYSICAL components m_r = rho v_r, m_theta = rho v_theta: d_t m_r + (1/r) d_r(r (rho v_r^2 + p)) + (1/r) d_theta(rho v_r v_theta)

(rho v_theta^2 + p)/r = 0 (CENTRIFUGAL + pressure term) d_t m_theta + (1/r) d_r(r rho v_r v_theta) + (1/r) d_theta(rho v_theta^2 + p)
(rho v_r v_theta)/r = 0 (cross CURVATURE term) The assemble_rhs_polar operator computes EXACTLY -(1/r) d_r(r F_r) - (1/r) d_theta(F_theta) with F_r, F_theta = IsothermalFlux::flux: it thus reproduces the divergences, but NOT the algebraic terms -(rho v_theta^2 + p)/r and +(rho v_r v_theta)/r. These terms are NOT captured by the conservative divergence (proof: on the cell (rho, v_r=0, v_theta(r)) in rotational equilibrium d_r p = rho v_theta^2/r, the radial divergence alone would yield d_t m_r = -(d_r p + p/r) != 0, breaking the equilibrium). An explicit GEOMETRIC SOURCE is therefore REQUIRED, provided here and added per cell by assemble_rhs_polar (which alone knows r): S_geom = ( 0 , (rho v_theta^2 + p)/r , -(rho v_r v_theta)/r ). With this source the rotational equilibrium is preserved to the scheme order (cf. test_polar_fluid_equilibrium). r > 0 (ring, r_min > 0): no axis singularity.

CONTRACT: pointwise PHYSICAL brick, device-callable (POPS_HD), no box, no allocation. polar_geom_source takes ONLY the state and r (no aux): it is pure metric.

Member Function Documentation

◆ polar_geom_source()

POPS_HD StateVec< 3 > pops::IsothermalFluxPolar::polar_geom_source	(	const StateVec< 3 > &	u,
		Real	r
	)		const

inline

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

include/pops/physics/bricks/hyperbolic.hpp

IsothermalFluxPolar Struct Reference¶

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ polar_geom_source()