A general existence result for isothermal two-phase flows with phase transition

Liquid-vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in (Quarterly of applied Mathematics, vol.\ LXXI 3 (2013), pp.\ 509-540.). This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of the present work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and evaporation are discussed

On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM)

Three methods are reviewed for computing optimal weights and abscissas which can be used in the Quadrature Method of Moments (QMOM): the Product-Difference Algorithm (PDA), the Long Quotient-Modified Difference Algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub--Welsch Algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA

On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM)

Three methods are reviewed for computing optimal weights and abscissas which can be used in the Quadrature Method of Moments (QMOM): the Product-Difference Algorithm (PDA), the Long Quotient-Modified Difference Algorithm (LQMDA, variants are also called Wheeler algorithm or Chebyshev algorithm), and the Golub--Welsch Algorithm (GWA). The PDA is traditionally used in applications. It is discussed that the PDA fails in certain situations whereas the LQMDA and the GWA are successful. Numerical studies reveal that the LQMDA is also more efficient than the PDA

Boundary Feedback Control for Hyperbolic Systems

We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems $\mathbb{R}^d$. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $L^2$ for the arising system using a suitable feedback control. We show the applicability discussing the barotropic Euler equations.Comment: arXiv admin note: text overlap with arXiv:2207.1200

Explicit-Implicit Domain Splitting for Two Phase Flows with Phase Transition

Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The phase interface is modeled as a sharp interface and the mass transfer across the phase boundary is modeled by a kinetic relation. Existence and uniqueness results were proven in Ref. \cite{Hantke2019a}. Using sharp interfaces for simulating nucleation and cavitation results in the grid containing tiny cells that are several orders of magnitude smaller than the remaining grid cells. This forces explicit time stepping schemes to take tiny time steps on these cells. As a remedy we suggest an explicit implicit domain splitting where the majority of the grid cells is treated explicitly and only the neighborhood of the tiny cells is treated implicitly. We use dual time stepping to solve the resulting small implicit systems. Our numerical results indicate that the new scheme is robust and provides significant speed-up compared to a fully explicit treatment

Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions

The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and three space dimensions. Of particular interest in the solutions are the formation of shock waves and a pressure blow up. For the investigation of these phenomena we develop a one-dimensional scheme using radial symmetry and integral conservation laws. We compare the numerical results with solutions of multi-dimensional high-order numerical schemes for general initial data in two space dimensions. The presented test cases and results may serve as interesting benchmark tests for multi-dimensional solvers.Comment: arXiv admin note: text overlap with arXiv:2002.0118

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The model is a simplified case of the seven-equation Baer-Nunziato model of compressible multi-phase flows, and results in a nonlinear hyperbolic system with non-conservative products. The geometry of the solid bodies is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume. This allows the discretization of arbitrarily complex geometries on simple uniform or adaptive Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero, while it is unitary in the fluid phase. We prove that at the material interface, i.e. where the volume fraction jumps from unity to zero, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity. This result can be directly derived from the governing equations, either via Riemann invariants or from the generalized Rankine Hugoniot conditions according to the theory of Dal Maso, Le Floch and Murat, which justifies the use of a path-conservative approach for treating the nonconservative products. The governing equations of our new model are solved on uniform Cartesian grids via a high order path-conservative ADER discontinuous Galerkin (DG) method with a posteriori sub-cell finite volume (FV) limiter. Since the numerical method is of the shock capturing type, the fluid-solid boundary is never explicitly tracked by the numerical method, neither via interface reconstruction, nor via mesh motion. The effectiveness of the proposed approach is tested on a set of numerical test problems, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies

Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions

The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimension- less four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and three space dimensions. Of particular interest in the solutions are the formation of shock waves and a pressure blow up. For the investigation of these phenomena we develop a one-dimensional scheme using radial symmetry and integral conservation laws. We compare the numerical results with solutions of multi-dimensional high-order numerical schemes for general initial data in two space dimensions. The presented test cases and results may serve as interesting benchmark tests for multi-dimensional solvers

Contributions of mean and shape of blood pressure distribution to worldwide trends and variations in raised blood pressure: A pooled analysis of 1018 population-based measurement studies with 88.6 million participants

© The Author(s) 2018. Background: Change in the prevalence of raised blood pressure could be due to both shifts in the entire distribution of blood pressure (representing the combined effects of public health interventions and secular trends) and changes in its high-blood-pressure tail (representing successful clinical interventions to control blood pressure in the hypertensive population). Our aim was to quantify the contributions of these two phenomena to the worldwide trends in the prevalence of raised blood pressure. Methods: We pooled 1018 population-based studies with blood pressure measurements on 88.6 million participants from 1985 to 2016. We first calculated mean systolic blood pressure (SBP), mean diastolic blood pressure (DBP) and prevalence of raised blood pressure by sex and 10-year age group from 20-29 years to 70-79 years in each study, taking into account complex survey design and survey sample weights, where relevant. We used a linear mixed effect model to quantify the association between (probittransformed) prevalence of raised blood pressure and age-group- and sex-specific mean blood pressure. We calculated the contributions of change in mean SBP and DBP, and of change in the prevalence-mean association, to the change in prevalence of raised blood pressure. Results: In 2005-16, at the same level of population mean SBP and DBP, men and women in South Asia and in Central Asia, the Middle East and North Africa would have the highest prevalence of raised blood pressure, and men and women in the highincome Asia Pacific and high-income Western regions would have the lowest. In most region-sex-age groups where the prevalence of raised blood pressure declined, one half or more of the decline was due to the decline in mean blood pressure. Where prevalence of raised blood pressure has increased, the change was entirely driven by increasing mean blood pressure, offset partly by the change in the prevalence-mean association. Conclusions: Change in mean blood pressure is the main driver of the worldwide change in the prevalence of raised blood pressure, but change in the high-blood-pressure tail of the distribution has also contributed to the change in prevalence, especially in older age groups