Generalized slope limiter for dG methods. More...

Public Member Functions
	CSRSlopeLimiter (real_type mod=(real_type) 0)

DG_DEVICE void	operator() (unsigned i, const int row_offsets, const int column_indices, const real_type values, const real_type x, real_type *y)

Detailed Description

template<class real_type>
struct dg::CSRSlopeLimiter< real_type >

Generalized slope limiter for dG methods.

Consider the one-dimensional case. The first step is to transform the given values to compute modal coefficients. The linear part is given by \( u_h^1(x) = u_{n0}p_{n0}(x) + u_{n1}p_{n1}(x)\) with \(p_{n0}(x) = 1\) and \( p_{n1}(x) = 2(x-x_n)/h\). Then the limiter is defined via

\[ \Lambda\Pi ( u_h^1)|_n = u_{n0} + \textrm{minmod}\left( u_{n1}, ( u_{(n+1)0} - u_{n0}), (u_{(n)0} - u_{(n-1)0})\right)p_{n1}(x) \]

If the result of the minmod function is \( u_{n1}\), then \( \Lambda\Pi( u_h)|_n = u_h|_n\), else \( \Lambda\Pi(u_h)|_n = \Lambda\Pi(u_h^1)|_n\) Must be applied in combination with limiter_stencil

Note: This limiter in a dG advection scheme has mixed success, generally maybe because we use it as a Kronecker product of two 1d filters?

See also: dg::blas2::stencil dg::create::limiter_stencil

Constructor & Destructor Documentation

◆ CSRSlopeLimiter()

template<class real_type >

dg::CSRSlopeLimiter< real_type >::CSRSlopeLimiter ( real_type mod = (real_type)0 )

inline

Member Function Documentation

◆ operator()()