DiFfRG::def::VanAlbadaLimiter Class Reference

van Albada (1982) slope limiter — second-order TVD and C¹ in u. More...

#include <van_albada_limiter.hh>

Static Public Member Functions
template<typename NumberType >
static NumberType	slope_limit (const NumberType &a, const NumberType &b)

Detailed Description

van Albada (1982) slope limiter — second-order TVD and C¹ in u.

Functional form (van Albada–van Leer–Roberts): phi(a, b) = ((a² + ε) · b + (b² + ε) · a) / (a² + b² + 2ε) when a·b > 0, = 0 otherwise.

Equivalent compact form used here: phi(a, b) = step(a·b) · (a · b² + b · a²) / (a² + b² + ε_floor)

Key properties used by this project:

• C¹ in (a, b) on the strict interior of {a·b > 0}: numerator and denominator are both polynomials, and the denominator is bounded away from zero by ε_floor.
• TVD: limited slope vanishes when slopes disagree in sign.
• Smooth-extremum: reduces to (a + b)/2 when a ≈ b > 0 (no clipping at smooth extrema, unlike MinMod).

Diagnostic motivation: MinMod is C⁰ but NOT C¹ in u (sign-change kink AND magnitude-tie kink). SUNDIALS IDA's Newton iteration needs at least a locally Lipschitz Jacobian to converge; MinMod's kinks cause the apparent Jacobian to flip by O(1) inside O(ε) perturbations of the state, which stalls the implicit integrator. van Albada removes the magnitude-tie kink entirely and leaves only the (much less frequently crossed) sign-change boundary.

Note: the sign-change boundary a·b = 0 is implemented here via a branch (the ternary). If even that one kink is too sharp for IDA, a softplus regularisation phi · 0.5·(1 + tanh(a·b/δ)) is a drop-in upgrade — but try the cleaner form first.

Member Function Documentation

slope_limit()

template<typename NumberType >

static NumberType DiFfRG::def::VanAlbadaLimiter::slope_limit ( const NumberType & a, const NumberType & b )

inlinestatic

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

• /home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/discretization/FV/limiter/van_albada_limiter.hh