A pressure-stabilized formulation of incompressible flow problems on anisotropic finite-element meshes

We consider a pressure stabilized, finite element approximation of incompressible flow problems in primitive velocity--pressure variables, which is based on a projection of the gradient of the discrete pressure onto the space of discrete functions. Equal order interpolation for the velocity and the pressure can be employed with this formulation. The method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios

Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations

In this paper we analyse a pressure stabilized, finite element method for the unsteady, incompressible Navier-Stokes equations in primitive variables; for the time discretization we focus on a fully implicit, monolithic scheme. We provide some error estimates for the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces L^2(W) and H(W) the pressure solution is shown to be order 1/2 accurate in the time step and also optimal in the mesh size. These estimates are proved assuming only a weak compatibility condition on the approximating spaces of velocity and pressure, which is satisfied by equal order interpolations

Analysis of fractional step, finite element methods for the incompressible navier-stokes equations

En la presente tesis se han estudiado métodos de paso fraccionado para la resolución numérica de la ecuación de Navier-Stokes incompresible mediante el método de los elementos finitos; dicha ecuación rige el movimiento de un fluido incompresible viscoso. Partiendo del análisis del método de proyección clásico, se desarrolla un método para el problema de Stokes (lineal y estacionario) con iguales propiedades en cuanto a discretizacion espacial que aquel, explicando así sus propiedades de estabilización de la presión. Se da también una extensión del nuevo método a la ecuación de Navier-Stokes incompresible estacionaria (no lineal).En la segunda parte de la tesis, se desarrolla un método de paso fraccionado para el problema de evolución que supera un inconveniente del método de proyección relativo a la imposición de las condiciones de contorno.Para todos los métodos desarrollados, se demuestran teoremas de convergencia y estimaciones de error, se proponen implementaciones eficientes y se proporcionan numerosos resultados numéricos

An implicit finite-element model for 3D non-hydrostatic mesoscale ocean flows

We present in this paper a pressure stabilized, finite element method for the numerical approximation of three-dimensional, non-hydrostatic mesoscale ocean flows. The model considered here incorporates surface wind stress, bottom friction and Coriolis acceleration, and it is applicable to irregular bottom topographies. An implicit unconditionally stable scheme is employed for the time advancement and an anisotropic stabilization technique is used for the spatial finite element discretization. The numerical results obtained on test cases demonstrate the robustness and accuracy of the method proposed here

Aproximación del problema de Stokes mediante elementos finitos mixtos de tipo cross-grid

En esta comunicación introducimos una familia de métodos de elementos finitos mixtos para la resolución numérica del problema de Stokes en dimensión 2. En estos métodos, la presión se interpola en una malla de elementos cuadriláteros, mientras que la velocidad se interpola en una malla de elementos triangulares obtenida subdividiendo cada cuadrilátero en cuatro triángulos por sus diagonales. Se consideran entonces interpolaciones de grado k para las velocidades y grado l para la presión, siendo k ≥ l ≥ 1. Por todo ello, estos elementos se han denominado de tipo cross-grid PkQl (ver [3]). Se presenta un análisis numérico de la estabilidad de estos métodos para elementos rectangulares, basado en la técnica de los macroelementos de Stenberg (ver [4], [5], [6]), y se analizan en particular los casos de orden menor, P1Q1 y P2Q1. En el primer caso, se demuestra la existencia de un modo espurio global para la presión, de manera que este elemento no es estable. En el segundo caso se demuestra la estabilidad del método, y por tanto su convergencia óptima. Se presentan también resultados numéricos obtenidos con estos elementos en varios casos test, tanto con mallas de elementos rectangulares como de cuadriláteros generales. Dichos resultados confirman la existencia del modo espurio de presión para el elemento P1Q1 y la estabilidad del elemento P2Q1.Postprint (published version

Finite element approximation of 3D non-hydrostatic turbulent coastal ocean flows using a LES model

In this paper we present a stabilized finite element method for three-dimensional, non-hydrostatic, turbulent coastal ocean flows. The model we have developed, named HELIKE, incorporates also surface wind stress, bottom friction, Coriolis forces and several closure models for both the horizontal and the vertical turbulent eddy vis- cosity coefficients. Unstructured meshes are employed so that complex geometries can be accurately approximated, and implicit time stepping allows to use large time steps. Numerical results are presented in various test cases, in which comparisons between different turbulence models are provided

Numerical simulation of the dispersion of contaminants by a characteristic-based method with applications to the Ebro delta and the Huelva estuary

In this paper we consider an explicit, characteristic-based method for the numerical simulation of the dispersion of contaminants in a fluid medium. A quasi-3D formulation is employed for the spatial approximation. Two real-life applications of the model developed are presented: the dispersion of the plume of the Ebro river and the thermal outflow of power plants in the Huelva estuary

Comparison of seven prognostic tools to identify low-risk pulmonary embolism in patients aged <50 years

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The evolution of the ventilatory ratio is a prognostic factor in mechanically ventilated COVID-19 ARDS patients

Background: Mortality due to COVID-19 is high, especially in patients requiring mechanical ventilation. The purpose of the study is to investigate associations between mortality and variables measured during the first three days of mechanical ventilation in patients with COVID-19 intubated at ICU admission. Methods: Multicenter, observational, cohort study includes consecutive patients with COVID-19 admitted to 44 Spanish ICUs between February 25 and July 31, 2020, who required intubation at ICU admission and mechanical ventilation for more than three days. We collected demographic and clinical data prior to admission; information about clinical evolution at days 1 and 3 of mechanical ventilation; and outcomes. Results: Of the 2,095 patients with COVID-19 admitted to the ICU, 1,118 (53.3%) were intubated at day 1 and remained under mechanical ventilation at day three. From days 1 to 3, PaO2/FiO2 increased from 115.6 [80.0-171.2] to 180.0 [135.4-227.9] mmHg and the ventilatory ratio from 1.73 [1.33-2.25] to 1.96 [1.61-2.40]. In-hospital mortality was 38.7%. A higher increase between ICU admission and day 3 in the ventilatory ratio (OR 1.04 [CI 1.01-1.07], p = 0.030) and creatinine levels (OR 1.05 [CI 1.01-1.09], p = 0.005) and a lower increase in platelet counts (OR 0.96 [CI 0.93-1.00], p = 0.037) were independently associated with a higher risk of death. No association between mortality and the PaO2/FiO2 variation was observed (OR 0.99 [CI 0.95 to 1.02], p = 0.47). Conclusions: Higher ventilatory ratio and its increase at day 3 is associated with mortality in patients with COVID-19 receiving mechanical ventilation at ICU admission. No association was found in the PaO2/FiO2 variation