Standard SPH interpolation heavily depends on the basic premise that each particle has the so called full support.
Full support implies that the owner particles can see particles all around itself within the smoothing length of the
particle, which mathematically implies that the sum of the kernel, also known as Shepard coefficient, is equal
to one.
The Riemann problem can be defined as a category of initial value problems that involve a conservation equation and
a piecewise data set with a single discontinuity.
Riemann Particle Interaction Scheme
The Riemann problem can be defined as a category of initial value problems that involve a conservation equation and a piecewise data set with a single discontinuity.