We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate...

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...