scholarly journals A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles

2014 ◽  
Vol 24 (10) ◽  
pp. 2043-2083 ◽  
Author(s):  
Frédéric Coquel ◽  
Khaled Saleh ◽  
Nicolas Seguin
Keyword(s):  
Cross Section ◽  
Gas Dynamics ◽  
Numerical Scheme ◽  
Fluid Flows ◽  
Finite Volume Scheme ◽  
Riemann Solver ◽  
Time Step ◽  
Piecewise Constant ◽  
Entropy Satisfying ◽  
Do So

We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the cross-section and on an approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous sections with arbitrary large jumps. To do so, we introduce, in the first step of the relaxation solver, a singular dissipation measure superposed on the standing wave, which enables us to control the approximate speeds of sound and thus the time step, even for extreme initial data.

A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

2011 ◽  
Vol 9 (1) ◽  
pp. 205-230 ◽  
Author(s):  
Angela Ferrari ◽  
Claus-Dieter Munz ◽  
Bernhard Weigand
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Indicator Function ◽  
Finite Volume Scheme ◽  
Riemann Solver ◽  
Time Step ◽  
Material Interface ◽  
Volume Scheme ◽  
Time Stepping ◽  
Local Time Stepping

AbstractIn this paper, a new sharp-interface approach to simulate compressible multiphase flows is proposed. The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order path-conservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface. At the interface our method applies ghost cells to compute the numerical flux, as the ghost fluid method. However, unlike the original ghost fluid scheme of Fedkiw et al. [15], the state of the ghost fluid is derived from an approximate-state Riemann solver, similar to the approach proposed in [25], but based on a much simpler formulation. Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface, instead of the system used in [25]. Away from the interface, we use the new general Osher-type flux recently proposed by Dumbser and Toro [13], which is a simple but complete Riemann solver, applicable to general hyperbolic conservation laws. The time integration is performed using a fully-discrete one-step scheme, based on the approaches recently proposed in [5,7]. This allows us to evolve the system also with time-accurate local time stepping. Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme, a local evolution for the indicator function is applied, which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step. The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme. Two different fluids have been used, namely an ideal gas and a weakly compressible fluid modeled by the Tait equation. Several tests have been computed to assess the accuracy and the performance of the new high order scheme. A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions. The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.

scholarly journals A new two-columns description for convective transport in stars

2008 ◽  
Vol 4 (S252) ◽  
pp. 89-95
Author(s):  
Alexander Stökl
Keyword(s):  
Fluid Flow ◽  
Velocity Field ◽  
Cross Section ◽  
Numerical Scheme ◽  
Convective Transport ◽  
Radiation Hydrodynamics ◽  
Convective Velocity ◽  
Time Step ◽  
Geometrical Meaning ◽  
Convective Cells

AbstractAssuming that the largest convective patterns generate the majority of convective transport, we devise a numerical scheme simplifying the convective velocity field using two parallel radial columns to represent up- and downstream flows. Horizontal exchange is described by fluid flow and radiation over the interface between those two columns. The main parameters of this convective description have a straightforward geometrical meaning, namely the diameter of the columns (representing the size of the convective cells) and the ratio of cross section between up- and downdrafts. For this geometrical setup, the equations of radiation hydrodynamics are solved time-dependently using an implicit scheme which has the advantage of being devoid of any time step limits. In order to demonstrate our approach, we present comparisons with detailed 2D hydrodynamics computations for the example of convection zones in Cepheids.

scholarly journals An All-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes

2016 ◽  
Vol 20 (1) ◽  
pp. 188-233 ◽  
Author(s):  
Christophe Chalons ◽  
Mathieu Girardin ◽  
Samuel Kokh
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Gas Dynamics ◽  
Numerical Scheme ◽  
Natural Extension ◽  
Mesh Size ◽  
Approximate Solutions ◽  
Entropy Inequality ◽  
Gas Dynamics Equations ◽  
Time Step

AbstractWe propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals A Middleware-Based Approach for Multi-Scale Mobility Simulation

2021 ◽  
Vol 13 (2) ◽  
pp. 22
Author(s):  
Xavier Boulet ◽  
Mahdi Zargayouna ◽  
Gérard Scemama ◽  
Fabien Leurent
Keyword(s):  
Modeling And Simulation ◽  
Transportation Networks ◽  
External Control ◽  
Independent Mobility ◽  
Time Step ◽  
Time Representation ◽  
Multi Scale ◽  
Networks Analysis ◽  
Maximal Benefit ◽  
Do So

Modeling and simulation play an important role in transportation networks analysis. In the literature, authors have proposed many traffic and mobility simulations, with different features and corresponding to different contexts and objectives. They notably consider different scales of simulations. The scales refer to the represented entities, as well as to the space and the time representation of the transportation environment. However, we often need to represent different scales in the same simulation, for instance to represent a neighborhood interacting with a wider region. In this paper, we advocate for the reuse of existing simulations to build a new multi-scale simulation. To do so, we propose a middleware model to couple independent mobility simulations, working at different scales. We consider all the necessary processing and workflow to allow for a coherent orchestration of these simulations. We also propose a prototype implementation of the middleware. The results show that such a middleware is capable of creating a new multi-scale mobility simulation from existing ones, while minimizing the incoherence between them. They also suggest that, to have a maximal benefit from the middleware, existing mobility simulation platforms should allow for an external control of the simulations, allowing for executing a time step several times if necessary.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

Dissipation Improvement of MUSCL Scheme for Computational Aeroacoustics

2001 ◽  
Vol 17 (1) ◽  
pp. 39-47
Author(s):  
San-Yin Lin ◽  
Sheng-Chang Shih ◽  
Jen-Jiun Hu
Keyword(s):  
Wave Interaction ◽  
Sine Wave ◽  
Numerical Dissipation ◽  
Finite Volume Scheme ◽  
Linear Wave ◽  
Riemann Solver ◽  
Two Dimensional ◽  
Order Accuracy ◽  
Upwind Schemes ◽  
Continuous Waves

ABSTRACTAn upwind finite-volume scheme is studied for solving the solutions of two dimensional Euler equations. It based on the MUSCL (Monotone Upstream Scheme for Conservation Laws) approach with the Roe approximate Riemann solver for the numerical flux evaluation. First, dissipation and dispersion relation, and group velocity of the scheme are derived to analyze the capability of the proposed scheme for capturing physical waves, such as acoustic, entropy, and vorticity waves. Then the scheme is greatly enhanced through a strategy on the numerical dissipation to effectively handle aeroacoustic computations. The numerical results indicate that the numerical dissipation strategy allows that the scheme simulates the continuous waves, such as sound and sine waves, at fourth-order accuracy and captures the discontinuous waves, such a shock wave, sharply as well as most of upwind schemes do. The tested problems include linear wave convection, propagation of a sine-wave packet, propagation of discontinuous and sine waves, shock and sine wave interaction, propagation of acoustic, vorticity, and density pulses in an uniform freestream, and two-dimensional traveling vortex in a low-speed freestream.

scholarly journals MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma

2018 ◽  
Vol 615 ◽  
pp. A67 ◽  
Author(s):  
P. A. González-Morales ◽  
E. Khomenko ◽  
T. P. Downes ◽  
A. de Vicente
Keyword(s):  
Numerical Scheme ◽  
Operator Splitting ◽  
Conservation Equation ◽  
Ambipolar Diffusion ◽  
Point Of View ◽  
Integration Time ◽  
Solar Photosphere ◽  
Time Step ◽  
Diffusion Term ◽  
Fluid Approximation

The interaction of plasma with magnetic field in the partially ionised solar atmosphere is frequently modelled via a single-fluid approximation, which is valid for the case of a strongly coupled collisional media, such as solar photosphere and low chromosphere. Under the single-fluid formalism the main non-ideal effects are described by a series of extra terms in the generalised induction equation and in the energy conservation equation. These effects are: Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery effect. From the point of view of the numerical solution of the single-fluid equations, when ambipolar diffusion or Hall effects dominate can introduce severe restrictions on the integration time step and can compromise the stability of the numerical scheme. In this paper we introduce two numerical schemes to overcome those limitations. The first of them is known as super time-stepping (STS) and it is designed to overcome the limitations imposed when the ambipolar diffusion term is dominant. The second scheme is called the Hall diffusion scheme (HDS) and it is used when the Hall term becomes dominant. These two numerical techniques can be used together by applying Strang operator splitting. This paper describes the implementation of the STS and HDS schemes in the single-fluid code MANCHA3D. The validation for each of these schemes is provided by comparing the analytical solution with the numerical one for a suite of numerical tests.

scholarly journals On the Temperature Distribution Inside a Tree Under Fire Conditions

1991 ◽  
Vol 1 (2) ◽  
pp. 87 ◽  
Author(s):  
JJ Costa ◽  
LA Oliveira ◽  
DX Viegas ◽  
LP Neto
Keyword(s):  
Cross Section ◽  
Heat Conduction Equation ◽  
Numerical Scheme ◽  
Unit Length ◽  
Circular Cross Section ◽  
Time Dependent ◽  
Tree Trunk ◽  
Temperature Field Distribution ◽  
Ground Fire ◽  
Fire Conditions

A simple and efficient numerical scheme is presented for the prediction of temperature field distribution inside a tree trunk subjected to ground fire conditions. The trunk is modelled by a cylinder of circular cross section and unit length, through which the time-dependent heat conduction equation is numerically integrated. The model is partly validated in laboratory and then applied to the case of a prescribed ground fire inside a Pinus pinmter stand.

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