scholarly journals Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

2021 ◽  
Author(s):  
Václav Kučera ◽  
Mária Lukáčová-Medvid’ová ◽  
Sebastian Noelle ◽  
Jochen Schütz
Keyword(s):  
Asymptotic Properties ◽  
Reference State ◽  
Math Model ◽  
Implicit Schemes ◽  
Comput Phys ◽  
Weakly Compressible ◽  
Hilbert Expansion ◽  
Imex Schemes ◽  
Numer Anal ◽  
The One

AbstractIn this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

Modelling lymph flow in the lymphatic system: from 0D to 1D spatial resolution

2018 ◽  
Vol 13 (5) ◽  
pp. 45 ◽  
Author(s):  
Rufina M. Tretyakova ◽  
Gennady I. Lobov ◽  
Gennady A. Bocharov
Keyword(s):  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Published Data ◽  
Modeling Tools ◽  
Math Model ◽  
Flow Models ◽  
Modelling Studies ◽  
1D Model ◽  
Numer Anal ◽  
The One

In this study, we formulated a core mathematical model for describing the one-dimensional lymph flow in lymphatic vessels and branching network of lymphatic vessels. The 1D model was numerically implemented using the 1D haemodynamic modeling tools developed in T.M. Gamilov et al. and S. Simakov et al. [T.M. Gamilov et al., Transl. Med. 6 (2013) 5–13 and S. Simakov et al., Russian J. Numer. Anal. Math. Model. 28 (2013) 485–504]. The formulated model was calibrated using published data on lymph flow dynamics and other modelling studies of lymph flows. The comparison of 0D and 1D formulations of the lymph flow models is presented.

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

scholarly journals Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography

2005 ◽  
Vol 133 (5) ◽  
pp. 1065-1075 ◽  
Author(s):  
P. Bénard ◽  
J. Mašek ◽  
P. Smolíková
Keyword(s):  
Euler Equations ◽  
Evolution Equations ◽  
Momentum Equation ◽  
Primitive Equations ◽  
Prognostic Variables ◽  
Flat Terrain ◽  
Implicit Schemes ◽  
Constant Coefficients ◽  
The Stability ◽  
The One

Abstract The stability of constant-coefficients semi-implicit schemes for the hydrostatic primitive equations and the fully elastic Euler equations in the presence of explicitly treated thermal residuals has been theoretically examined in the earlier literature, but only for the case of a flat terrain. This paper extends these analyses to a case in which an orography is present, in the shape of a uniform slope. It is shown, with mass-based coordinates, that for the Euler equations, the presence of a slope reduces furthermore the set of the prognostic variables that can be used in the vertical momentum equation to maintain the robustness of the scheme, compared to the case of a flat terrain. The situation appears to be similar for systems cast in mass-based and height-based vertical coordinates. Still for mass-based vertical coordinates, an optimal prognostic variable is proposed and is shown to result in a robustness similar to the one observed for the hydrostatic primitive equations system. The prognostic variables that lead to robust semi-implicit schemes share the property of having cumbersome evolution equations, and an alternative time treatment of some terms is then required to keep the evolution equation reasonably simple. This treatment is shown not to modify substantially the stability of the time scheme. This study finally indicates that with a pertinent choice for the prognostic variables, mass-based vertical coordinates are equally suitable as height-based coordinates for efficiently solving the compressible Euler equations system.

scholarly journals A WCSPH Particle Shifting Strategy for Simulating Violent Free Surface Flows

Water ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 3189
Author(s):  
Abdelkader Krimi ◽  
Mojtaba Jandaghian ◽  
Ahmad Shakibaeinia
Keyword(s):  
Free Surface ◽  
Surface Region ◽  
Free Surface Flows ◽  
Sph Method ◽  
Surface Flows ◽  
Weakly Compressible ◽  
Shifting Strategy ◽  
Long Time ◽  
The One ◽  
Stability And Consistency

In this work, we develop an enhanced particle shifting strategy in the framework of weakly compressible δ+-SPH method. This technique can be considered as an extension of the so-called improved particle shifting technology (IPST) proposed by Wang et al. (2019). We introduce a new parameter named “ϕ” to the particle shifting formulation, on the one hand to reduce the effect of truncated kernel support on the formulation near the free surface region, on the other hand, to deal with the problem of poor estimation of free surface particles. We define a simple criterion based on the estimation of particle concentration to limit the error’s accumulation in time caused by the shifting in order to achieve a long time violent free surface flows simulation. We propose also an efficient and simple concept for free surface particles detection. A validation of accuracy, stability and consistency of the presented model was shown via several challenging benchmarks.

scholarly journals Time-Adaptive Statistical Test for Random Number Generators

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 630 ◽  
Author(s):  
Boris Ryabko
Keyword(s):  
Random Number ◽  
Statistical Tests ◽  
Asymptotic Properties ◽  
Test Sequence ◽  
P Value ◽  
Specific Test ◽  
Random Number Generators ◽  
P Values ◽  
Small Deviations ◽  
The One

The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, there are hundreds of RNG statistical tests that are often combined into so-called batteries, each containing from a dozen to more than one hundred tests. When a battery test is used, it is applied to a sequence generated by the RNG, and the calculation time is determined by the length of the sequence and the number of tests. Generally speaking, the longer is the sequence, the smaller are the deviations from randomness that can be found by a specific test. Thus, when a battery is applied, on the one hand, the “better” are the tests in the battery, the more chances there are to reject a “bad” RNG. On the other hand, the larger is the battery, the less time it can spend on each test and, therefore, the shorter is the test sequence. In turn, this reduces the ability to find small deviations from randomness. To reduce this trade-off, we propose an adaptive way to use batteries (and other sets) of tests, which requires less time but, in a certain sense, preserves the power of the original battery. We call this method time-adaptive battery of tests. The suggested method is based on the theorem which describes asymptotic properties of the so-called p-values of tests. Namely, the theorem claims that, if the RNG can be modeled by a stationary ergodic source, the value − l o g π ( x 1 x 2 … x n ) / n goes to 1 − h when n grows, where x 1 x 2 … is the sequence, π ( ) is the p-value of the most powerful test, and h is the limit Shannon entropy of the source.

scholarly journals Double Kernel Estimation of Sensitivities

2009 ◽  
Vol 46 (03) ◽  
pp. 791-811
Author(s):  
Romuald Elie
Keyword(s):  
Asymptotic Properties ◽  
Kernel Estimation ◽  
Score Function ◽  
Random Variable ◽  
Kernel Functions ◽  
Contingent Claim ◽  
Main Interest ◽  
Stringent Condition ◽  
Technical Interest ◽  
The One

In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.

scholarly journals HIGH-FIELD LIMIT OF THE VLASOV–POISSON–FOKKER–PLANCK SYSTEM: A COMPARISON OF DIFFERENT PERTURBATION METHODS

2001 ◽  
Vol 11 (08) ◽  
pp. 1457-1468 ◽  
Author(s):  
LUIS L. BONILLA ◽  
JUAN S. SOLER
Keyword(s):  
High Field ◽  
Three Dimensions ◽  
Field Limit ◽  
One Dimensional ◽  
System A ◽  
Reduced Equations ◽  
Hilbert Expansion ◽  
The One ◽  
Different Order ◽  
Fokker Planck

A reduced drift-diffusion (Smoluchowski–Poisson) equation is found for the electric charge in the high-field limit of the Vlasov–Poisson–Fokker–Planck system, both in one and three dimensions. The corresponding electric field satisfies a Burgers equation. Three methods are compared in the one-dimensional case: Hilbert expansion, Chapman–Enskog procedure and closure of the hierarchy of equations for the moments of the probability density. Of these methods, only the Chapman–Enskog method is able to systematically yield reduced equations containing terms of different order.

The Geometry of Dla: Different Aspects of the Departure from Self-Similarity

1994 ◽  
Vol 367 ◽  
Author(s):  
B.B. Mandelbrot ◽  
A. Vespignani ◽  
H. Kaufman
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Properties ◽  
Finite Size ◽  
Scaling Behavior ◽  
Self Similarity ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Large Numbers ◽  
The One

AbstractIn order to understand better the morphology and the asymptotic behavior in Diffusion Limited Aggregation (DLA), we studied a large numbers of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties, namely the moments of the particle's sticking distances and the scaling behavior of the transverse growth crosscuts, i.e., the one dimensional cuts by circles. The emerging picture for radial DLA departs from simple self-similarity for any finite size. It corresponds qualitatively to the scenario of infinite drift starting from the familiar five armed shape for small sizes and proceeding to an increasingly tight multi-armed shape. We show quantitatively how the lacunarity of circular clusters becomes increasingly “compact” with size. Finally, we find agreement among transverse cuts dimensions for clusters grown in different geometries, suggesting that the question of universality is best addressed on the crosscut.

Stability of a thermoelastic mixture with second sound

2018 ◽  
Vol 24 (6) ◽  
pp. 1692-1706 ◽  
Author(s):  
Margareth S. Alves ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
O. Vera Villagrán
Keyword(s):  
Initial Data ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Second Sound ◽  
Dimensional Model ◽  
One Dimensional ◽  
The One ◽  
Necessary And Sufficient

We consider the one-dimensional model of a thermoelastic mixture with second sound. We give a complete characterization of the asymptotic properties of the model in terms of the coefficients of the model. We establish the necessary and sufficient conditions for the model to be exponential or polynomial stable and also the conditions for which there exist initial data for where the energy is conserved.

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