num::spatial::debug::verify_kernel_normalization

Defined in header <spatial/debug.hpp>

template <class K, class Scalar = float>
requires smoothing_kernel<K, Scalar>
void verify_kernel_normalization(
    Scalar h, Scalar tol = Scalar(2e-2),
    std::source_location loc = std::source_location::current());

Verify that a smoothing kernel integrates to one over its support.

\[ \int_0^{2h} W(r,h) \, 2\pi r \, dr = 1 \]

SPH interpolates a field as \(\sum_j m_j (\rho_j)^{-1} A_j W_{ij}\), which reproduces a constant only when the kernel is normalized. A kernel that is not produces densities off by a constant factor, which looks like a physical result rather than an error.