High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order Report Title In this paper, spatially high-order Residual-Distribution (RD) schemes using the firstorder hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advectiondiffusion scheme was first intro...

In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate generalized Caputo fractional derivative (GCFD). Convergence order for (4−α), where α(0<α<1) of GCFD. The local truncation error also provided. Then, we adopt developed establish difference solution advection–diffusion equation with Dirichlet boundary conditions. Furthe...

This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the observer kernel equation is proved using the method of successive approximation.

Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time-scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate timeintegration. In particular, interesting regimes in combust...

An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element metho...

Many organisms search for limiting resources by using repeated responses to local cues, which cumulatively cause movement towards more favorable parts of their environment. This paper presents a general asymptotic expression, derived under the assumption of shallow environmental gradients, for the population-level flux of organisms moving at a constant speed and reorienting at rates determined ...

We discuss L integrability estimates for the solution u of the advection-diffusion equation ∂t u + div (bu) = ∆ u, where the velocity field b ∈ Lt r Lx q . We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examples.