We propose and analyze a new parallel paradigm that uses both the time space directions. The original approach couples Parareal algorithm with incomplete optimized Schwarz waveform relaxation (OSWR) iterations. analysis of this coupled method is presented for one-dimensional advection-reaction-diffusion equation. also prove general convergence result via energy estimates. Numerical results two-...

Abstract. We consider the problem of optimal mixing control. Our objective is to best enhance mixing by flow advection while the flow is optimized in the sense that it is almost steady and is of the least magnitude and the least rotation. For this we define a mixing efficiency functional by penalizing the average of variance of a diffusive scalar, the average of the flow, and the average of its...

We present a review of the semi-Lagrangian method for advection-diffusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator In...

We introduce a class of numerical schemes that preserve a discrete version of vorticity in conservation laws which involve grad advection. These schemes are based on reformulating finite volume schemes in terms of vertex centered numerical potentials. The resulting potential-based schemes have a genuinely multidimensional structure. A suitable choice of potentials leads to discrete vorticity pr...

The different kinds of boundary conditions for standard and fractional diffusion and advection diffusion equations are analyzed. Near the interface between two phases there arises a transition region which state differs from the state of contacting media owing to the different material particle interaction conditions. Particular emphasis has been placed on the conditions of nonperfect diffusive...

We introduce a class of numerical schemes that preserve a discrete version of vorticity in conservation laws which involve grad advection. These schemes are based on reformulating finite volume schemes in terms of vertex centered numerical potentials. The resulting potential-based schemes have a genuinely multidimensional structure. A suitable choice of potentials leads to discrete vorticity pr...

Conventional explicit nite diierence schemes for the advection equations are subject to the time step restrictions dictated by the CFL condition. In many situations, time step sizes are not chosen to satisfy accuracy requirements but rather to satisfy the CFL condition. In this paper we present explicit algorithms which are stable far beyond the CFL restriction. Similar or even better accuracy ...

We consider the influence of a shifting environment and an advection on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is shifting and without advection (β = 0), Du, Wei and Zhou in [16] showed that the species always dies out when the shifting speed c∗ ≥ C, and the long-time behavior of the species is det...

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise ...

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-dffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first or...