scholarly journals Computational simulation of one-dimensional waves with the Multigrid Method / Simulação computacional de ondas unidimensionais com o Método Multigrid

2021 ◽  
Vol 7 (8) ◽  
pp. 83763-83775
Author(s):  
Maicon F. Malacarne ◽  
Marcio A. V. Pinto ◽  
Sebastião R. Franco
Keyword(s):  
Multigrid Method ◽  
Computational Simulation ◽  
Computational Time ◽  
System Of Equations ◽  
Time Step ◽  
One Dimensional ◽  
Time Stepping ◽  
Engineering Problems ◽  
Large Systems ◽  
The Finite Difference Method

Several Engineering problems are modeled computationally, these simulations involve large systems, which are commonly difficult to solve. This paper deals with the simulation of one-dimensional waves, where the system resulting from the discretization by the Finite Difference Method is solved using the Multigrid Method with the conventional Gauss-Seidel solver, in order to decrease the computational time. Temporal discretization using the Time-Stepping method, where the system of equations is solved at each time step sequentially.

scholarly journals Comparison of numerical schemes of river flood routing with an inertial approximation of the Saint Venant equations

RBRH ◽  
2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Alice César Fassoni-Andrade ◽  
Fernando Mainardi Fan ◽  
Walter Collischonn ◽  
Artur César Fassoni ◽  
Rodrigo Cauduro Dias de Paiva
Keyword(s):  
Numerical Stability ◽  
Flood Routing ◽  
Computational Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Simple Formulation ◽  
One Dimensional ◽  
Saint Venant Equations ◽  
Original Scheme ◽  
The One

ABSTRACT The one-dimensional flow routing inertial model, formulated as an explicit solution, has advantages over other explicit models used in hydrological models that simplify the Saint-Venant equations. The main advantage is a simple formulation with good results. However, the inertial model is restricted to a small time step to avoid numerical instability. This paper proposes six numerical schemes that modify the one-dimensional inertial model in order to increase the numerical stability of the solution. The proposed numerical schemes were compared to the original scheme in four situations of river’s slope (normal, low, high and very high) and in two situations where the river is subject to downstream effects (dam backwater and tides). The results are discussed in terms of stability, peak flow, processing time, volume conservation error and RMSE (Root Mean Square Error). In general, the schemes showed improvement relative to each type of application. In particular, the numerical scheme here called Prog Q(k+1)xQ(k+1) stood out presenting advantages with greater numerical stability in relation to the original scheme. However, this scheme was not successful in the tide simulation situation. In addition, it was observed that the inclusion of the hydraulic radius calculation without simplification in the numerical schemes improved the results without increasing the computational time.

Semi-Elimination Methodology for Simulating High Flow Features in a Reservoir

2021 ◽  
Author(s):  
Yahan Yang ◽  
Ali Samii ◽  
Zhenlong Zhao ◽  
Guotong Ren
Keyword(s):  
High Flow ◽  
Small Cells ◽  
Computational Techniques ◽  
Computational Technique ◽  
System Of Equations ◽  
Time Step ◽  
Linear System Of Equations ◽  
Time Stepping ◽  
Model Complex ◽  
Upstream Weighting

Abstract Despite the rapid rise of computing power and advances in computational techniques in past decades, it is still challenging in reservoir simulation to model complex and detailed features that are represented by small cells with large permeability values, for example, fractures, multi-segment wells, etc. While those features may carry a large amount of flow and thus have a significant impact on the performance prediction, the combination of small volume and large permeability unfortunately leads to well-known time stepping and convergence difficulties during Newton iteration. We address this issue of high flow through small cells by developing a new semi-elimination computational technique. At the beginning of simulation, we construct a set of pressure basis which is a mapping from pressures at surrounding cells in the bulk of reservoir to pressures at those small cells. Next, we start the time-stepping scheme. For each time step or iteration within a time step, small cells are first employed to provide an accurate computation of flow rates and derivatives using upstream weighting and a flow partitioning scheme. Afterwards, small cells are eliminated and a linear system of equations is assembled and solved involving only bulk cells. This semi-elimination technique allows us to fundamentally avoid the drawbacks caused by including small cells in the global system of equations, while capturing their effect on the flow of hydrocarbon in the reservoir. One of the advantages of the proposed techniques over other existing methods is that it is fully implicit and preserves upstream weighting and compositions of the flow field even after small cells are eliminated, which enhances numerical stability and accuracy of simulation results. Application of this technique to several synthetic and field models demonstrates significant performance and accuracy improvement over standard approaches. This method thus offers a practical way to model complex and dynamic flow behaviors in important features without incurring penalties in speed and robustness of the simulation.

scholarly journals Revision of the convective transport module CVTRANS 2.4 in the EMAC atmospheric chemistry–climate model

2015 ◽  
Vol 8 (8) ◽  
pp. 2435-2445 ◽  
Author(s):  
H. G. Ouwersloot ◽  
A. Pozzer ◽  
B. Steil ◽  
H. Tost ◽  
J. Lelieveld
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Convective Transport ◽  
Computational Time ◽  
Cloud Base ◽  
Mixing Ratio ◽  
Time Step ◽  
Mixing Ratios ◽  
Time Stepping ◽  
Intermediate Time

Abstract. The convective transport module, CVTRANS, of the ECHAM/MESSy Atmospheric Chemistry (EMAC) model has been revised to better represent the physical flows and incorporate recent findings on the properties of the convective plumes. The modifications involve (i) applying intermediate time stepping based on a settable criterion, (ii) using an analytic expression to account for the intra-time-step mixing ratio evolution below cloud base, and (iii) implementing a novel expression for the mixing ratios of atmospheric compounds at the base of an updraft. Even when averaged over a year, the predicted mixing ratios of atmospheric compounds are affected considerably by the intermediate time stepping. For example, for an exponentially decaying atmospheric tracer with a lifetime of 1 day, the zonal averages can locally differ by more than a factor of 6 and the induced root mean square deviation from the original code is, weighted by the air mass, higher than 40 % of the average mixing ratio. The other modifications result in smaller differences. However, since they do not require additional computational time, their application is also recommended.

Transient Response in a One-Dimensional Model of Thermoelastic Contact

1996 ◽  
Vol 63 (3) ◽  
pp. 575-581 ◽  
Author(s):  
Z. S. Olesiak ◽  
Yu. A. Pyryev
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Transient Response ◽  
Computational Simulation ◽  
Linear Equations ◽  
Numerical Results ◽  
System Of Equations ◽  
Dimensional Model ◽  
One Dimensional ◽  
Method Of Solution

We consider two layers of different materials with the initial gap between them in the field of temperature with imperfect boundary conditions in Barber’s sense. The model we discuss is that of two contacting rods (Barber and Zhang, 1988) which in the case of a single rod was devised and discussed by Dundurs and Comninou (1976, 1979). In this paper we try to make a step further in the investigation of the essentially nonlinear problem. Though we consider a system of the linear equations of thermoelasticity the nonlinearity is induced by the boundary conditions dependent on the solution. We present an algorithm for solving the system of equations based on Laplace’s transform technique. The method of solution can be used also in the dynamical problems with inertial terms taken into account. The numerical results have been obtained by a kind of computational simulation.

A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

2014 ◽  
Vol 24 (3) ◽  
pp. 735-759 ◽  
Author(s):  
Anis Younes ◽  
Ahmed Makradi ◽  
Ali Zidane ◽  
Qian Shao ◽  
Lyazid Bouhala
Keyword(s):  
Natural Convection ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Discontinuous Galerkin ◽  
Truncation Error ◽  
Computational Time ◽  
Time Step ◽  
Content Type ◽  
Flow Problems ◽  
Time Stepping

Purpose – The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems. Design/methodology/approach – The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error. Findings – Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity. Originality/value – The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.

Calibration of a 1D/1D urban flood model using 1D/2D model results in the absence of field data

2011 ◽  
Vol 64 (5) ◽  
pp. 1016-1024 ◽  
Author(s):  
J. Leandro ◽  
S. Djordjević ◽  
A. S. Chen ◽  
D. A. Savić ◽  
M. Stanić
Keyword(s):  
Field Data ◽  
Computational Time ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Time Step ◽  
Urban Flood ◽  
One Dimensional ◽  
1D Model ◽  
Surface Network ◽  
2D Model

Recently increased flood events have been prompting researchers to improve existing coupled flood-models such as one-dimensional (1D)/1D and 1D/two-dimensional (2D) models. While 1D/1D models simulate sewer and surface networks using a one-dimensional approach, 1D/2D models represent the surface network by a two-dimensional surface grid. However their application raises two issues to urban flood modellers: (1) stormwater systems planning/emergency or risk analysis demands for fast models, and the 1D/2D computational time is prohibitive, (2) and the recognized lack of field data (e.g. Hunter et al. (2008)) causes difficulties for the calibration/validation of 1D/1D models. In this paper we propose to overcome these issues by calibrating a 1D/1D model with the results of a 1D/2D model. The flood-inundation results show that: (1) 1D/2D results can be used to calibrate faster 1D/1D models, (2) the 1D/1D model is able to map the 1D/2D flood maximum extent well, and the flooding limits satisfactorily in each time-step, (3) the 1D/1D model major differences are the instantaneous flow propagation and overestimation of the flood-depths within surface-ponds, (4) the agreement in the volume surcharged by both models is a necessary condition for the 1D surface-network validation and (5) the agreement of the manholes discharge shapes measures the fitness of the calibrated 1D surface-network.

scholarly journals Revision of the convective transport module CVTRANS 2.4 in the EMAC atmospheric chemistry–climate model

2015 ◽  
Vol 8 (4) ◽  
pp. 3117-3145
Author(s):  
H. G. Ouwersloot ◽  
A. Pozzer ◽  
B. Steil ◽  
H. Tost ◽  
J. Lelieveld
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Convective Transport ◽  
Computational Time ◽  
Cloud Base ◽  
Mixing Ratio ◽  
Time Step ◽  
Mixing Ratios ◽  
Time Stepping ◽  
Intermediate Time

Abstract. The convective transport module, CVTRANS, of the ECHAM/MESSy Atmospheric Chemistry (EMAC) model has been revised to better represent the physical flows and incorporate recent findings on the properties of the convective plumes. The modifications involve (i) applying intermediate time stepping based on a settable criterion, (ii) using an analytic expression to account for the intra time step mixing ratio evolution below cloud base, and (iii) implementing a novel expression for the mixing ratios of atmospheric compounds at the base of an updraft. Even when averaged over a year, the predicted mixing ratios of atmospheric compounds are significantly affected by the intermediate time stepping. For example, for an exponentially decaying atmospheric tracer with a lifetime of 1 day, the zonal averages can locally differ by more than a factor of 6 and the induced root mean square deviation from the original code is, weighted by the air mass, higher than 40% of the average mixing ratio. The other modifications result in smaller differences. However, since they do not require additional computational time, their application is also recommended.

Is Hydraulics Over-Used or Under-Used in Storm Drainage?

1994 ◽  
Vol 29 (1-2) ◽  
pp. 53-61
Author(s):  
Ben Chie Yen
Keyword(s):  
Unsteady Flow ◽  
Computational Time ◽  
Time Step ◽  
Flow Routing ◽  
Kinematic Wave Equation ◽  
Storm Drainage ◽  
Saint Venant Equations ◽  
Unsteady Flow Routing ◽  
Selection Of

Urban drainage models utilize hydraulics of different levels. Developing or selecting a model appropriate to a particular project is not an easy task. Not knowing the hydraulic principles and numerical techniques used in an existing model, users often misuse and abuse the model. Hydraulically, the use of the Saint-Venant equations is not always necessary. In many cases the kinematic wave equation is inadequate because of the backwater effect, whereas in designing sewers, often Manning's formula is adequate. The flow travel time provides a guide in selecting the computational time step At, which in turn, together with flow unsteadiness, helps in the selection of steady or unsteady flow routing. Often the noninertia model is the appropriate model for unsteady flow routing, whereas delivery curves are very useful for stepwise steady nonuniform flow routing and for determination of channel capacity.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Sign in / Sign up

Export Citation Format

Share Document