We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws. We compare the Kurganov-Tadmor (KT) two-dimensional (Kurganov and Tadmor, 2000) second order semi-discrete central scheme in dimension by dimension formulation with a new two-dimensional approach introduced here and applied in numerical simulations for two-phase, two-dimensional flows in heteroge...

A spectral vanishing viscosity technique (SVV) is presented for the simulation of 3D turbulent incompressible flows within a rotor–stator cavity. One characteristic of this technique is that the SVV is active only for the short length scales, a feature which is reminiscent of Large Eddy Simulation models. The Spectral Vanishing Viscosity, first introduced by E. Tadmor for the inviscid Burgers e...

We present VAH, a (3+1)-dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. solve hydrodynamic equations on an Eulerian grid using Kurganov-Tadmor algorithm combination new adaptive Runge-Kutta method. Our numerical scheme allows us to start soon after nuclear collision, largely avoid...

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs oscillations in the neighborhood of edges and an overall deterioration of the unacceptable first-order convergence in rate. The purpos...

Tibetan wild barley is a treasure trove of useful genes for crop improvement including abiotic stress tolerance, like drought. Root hair of single-celled structures plays an important role in water and nutrition uptake. Polyethylene-glycol-induced drought stress hydroponic/petri-dish experiments were performed, where root hair morphology and transcriptional characteristics of two contrasting Ti...

has been one of the most outstanding open problems. It plays a very important role in understanding the core problems in hydrodynamics such as the onset of turbulence (people have also tried to understand turbulence through studying weak solutions; see Scheffer, 1993 or Shnirelman, 1997). Much effort has been made to answer this question; see, e.g., Beale et al. (1984), Ebin et al. (1970), Cafl...

We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric flocking potential, the Cucker-Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor [14]. The main tools employed in the analysis are the velocity...

Tadmor, Nezzar and Vese [Eitan Tadmor, Suzanne Nezzar, and Luminita Vese. A multiscale image representation using hierarchical (BV, L2) decompositions. Multiscale Model. Simul., 2(4):554–579, 2004.] developed a total variation based multiscale method for decomposing a function f ∈ BV into a countable set of features {uk : k = 0, 1, 2 . . .} associated to a sequence of dyadic scales {λk = λ02−k ...

Entropy solutions have beenwidely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (AnnMath 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical sc...