Juan Luis Prieto

Anisotropic “Goal-Oriented” Mesh Adaptivity for Elliptic Problems

We propose in this paper an anisotropic, adaptive, finite element algorithm for steady, linear advection-diffusion-reaction problems with strong anisotropic features. The error analysis is based on the dual weighted residual methodology, allowing us to perform “goal-oriented” adaptation of a certain functional

A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

J(u)

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

of the solution and derive an “optimal” metric tensor for local mesh adaptation with linear and quadratic finite elements. As a novelty, and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles, we make use of a patchwise, higher-order interpolation recovery readily extendable to finite elements of arbitrary order. We carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal-oriented adaptive method. We compute the convergence rate and the effectivity index for a series of output functionals of the solution. The results show the good performance of the algorithm with linear as well as quadratic ...

A Stochastic Semi‐Lagrangian Micro‐Macro Model for Liquid Crystalline Solutions

A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.

A-SLEIPNNIR: A multiscale, anisotropic adaptive, particle level set framework for moving interfaces. Transport equation applications

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm,

Multi-scale Simulation of Newtonian and Non-Newtonian Multi-phase Flows

\parallel\cdot\parallel_{h,\infty}

An anisotropic, fully adaptive algorithm for the solution of convection-dominated equations with semi-Lagrangian schemes

, and the error analysis shows that when the level set solution

A semi-Lagrangian micro–macro method for viscoelastic flow calculations

u(t)

Stochastic particle level set simulations of buoyancy-driven droplets in non-Newtonian fluids

is in the Sobolev space

Stochastic semi-Lagrangian micro–macro calculations of liquid crystalline solutions in complex flows

W^{r+1,\infty}(D), r\geq 0