Related papers: Flux correction for nonconservative convection-dif…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
In this paper the projection hybrid FV/FE method presented in Busto et al. 2014 is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the $k-\varepsilon$ model. Regarding the…
We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the…
We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
This paper presents a data-driven framework for learning optimal second-order total variation diminishing (TVD) flux limiters via differentiable simulations. In our fully differentiable finite volume solvers, the limiter functions are…
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions,…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying the conventional second-order TVD schemes to the…
In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals,…
Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes…
The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. The…
Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed to suppress nonphysical oscillations. However, the…
Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from the non-convex nature of the optimization problem with multiple local optima, which usually requires a…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…