A MULTI-TIME-STEP STRATEGY BASED ON AN OPTIMIZED TIME INTERPOLATION SCHEME FOR OVERSET GRIDS

2010 ◽  
Vol 18 (02) ◽  
pp. 131-148 ◽  
Author(s):  
DAKAI LIN ◽  
MIN JIANG ◽  
XIAODONG LI
Keyword(s):  
Numerical Stability ◽  
Grid Generation ◽  
Interpolation Scheme ◽  
Time Step ◽  
Overset Grids ◽  
Numerical Examples ◽  
Typical Time ◽  
Time Marching

A multi-time-step strategy for overset grids is proposed based on an optimized time interpolation scheme. Time interpolation is adopted in the vicinity of the interface between adjacent blocks, which are marching in time with different time steps satisfying the local numerical stability. There is no strict constraint on the ratio of mesh sizes between neighboring blocks, and it can alleviate the burden of the grid generation for multi-time-step marching methods. The optimized time interpolation scheme can be simply combined with the existing typical time marching schemes to achieve multi-time-step marching for overset grids. Some numerical examples are presented to demonstrate the feasibility and efficiency of the proposed strategy.

Stability Analysis on the Algorithm of Constitutive Relation in Viscoplastic Materials

2016 ◽  
Vol 33 (2) ◽  
pp. 173-181
Author(s):  
M.-T. Liu ◽  
Y.-C. Li ◽  
X.-Z. Hu ◽  
J. Zhang ◽  
T.-G. Tang
Keyword(s):  
Numerical Calculation ◽  
Stability Analysis ◽  
Convergence Rate ◽  
Iterative Algorithm ◽  
Numerical Stability ◽  
Sufficient Condition ◽  
Time Step ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
The Stability

AbstractThe numerical stability of the explicit precise algorithm, which was developed for the viscoplastic materials, was analyzed. It was found that this algorithm is not absolutely stable. A necessary but not sufficient condition for the numerical stability was deduced. It showed that the time step in numerical calculation should be less than a certain value to guarantee the stability of explicit precise algorithm. Through a series of numerical examples, the stability analysis on the explicit precise algorithm was proved to be reliable. At last, an iterative algorithm was presented for viscoplastic materials. Both of the theoretical and numerical results showed that the iterative algorithm is unconditionally stable and its convergence rate is rapid. In practice, the explicit precise algorithm and iterative algorithm can be combined to obtain reliable results with the minimum computing costs.

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.

Surface grid generation methods for overset grids

1995 ◽  
Vol 24 (5) ◽  
pp. 509-522 ◽  
Author(s):  
William M. Chan ◽  
Pieter G. Buning
Keyword(s):  
Grid Generation ◽  
Overset Grids

A Successive Merging and Condensation (SMAC) Method Applied to Transient Analysis of Multi-Shaft Rotor System

1993 ◽  
Author(s):  
Santosh Ratan ◽  
Jorge Rodriguez
Keyword(s):  
Transient Response ◽  
Transient Analysis ◽  
Rotor System ◽  
Time Step ◽  
Transient Dynamic Analysis ◽  
Numerical Examples ◽  
Linear Coupling ◽  
Rotor Systems ◽  
Coupling Constraints ◽  
Smac Method

Abstract A method for performing transient dynamic analysis of multi-shaft rotor system is proposed. The proposed methodology uses the reported Successive Merge and Condensation (SMAC) method [12] and a decoupling technique to decouple the shafts. Multi-shaft rotor systems are treated as systems of many independent single shaft rotor systems with external unknown coupling forces acting at the points of couplings. For each time step, first, the SMAC method is used to get the transient response in terms of the unknown coupling forces. This is followed by the application of the coupling constraints to calculate the coupling forces and, in turn, the response at the end of that time step. The proposed method preserves the efficiency advantages of the SMAC algorithm for single-shaft rotor system. Numerical examples to validate and illustrate the applicability of the method are given. The method is shown to be applicable to linear and non-linear coupling problems.

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.

COMBINATION OF MESH DEFORMATION AND OVERSET GRID FOR SIMULATING UNSTEADY FLOW OF INSECT FLIGHT

2009 ◽  
Vol 23 (03) ◽  
pp. 525-528 ◽  
Author(s):  
TIANHANG XIAO ◽  
HAISONG ANG
Keyword(s):  
Insect Flight ◽  
Unsteady Flows ◽  
Flapping Wings ◽  
Mesh Deformation ◽  
Time Step ◽  
Overset Grids ◽  
Boundary Definition ◽  
Graph Mapping ◽  
Background Grid ◽  
Grid Cluster

As numerical simulation of unsteady flows due to moving boundaries such as flexible flapping-wings is difficult by conventional approaches, an effective strategy which combines mesh deformation based on Delaunay graph mapping and unstructured overset grids is proposed in this paper. A Delaunay graph is generated for each body-fitted grid cluster which overlaps or is embedded within an off-body background grid cluster. At each time step, the graph moves according to the wing's motion and deformation, and the grids move to new positions according to a one-to-one mapping between the graph and the grid. Then, intergrid-boundary definition is implemented automatically for computation.

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

Convergence of a highly accurate quasi-interpolation method for options pricing

2017 ◽  
Vol 04 (04) ◽  
pp. 1750048
Author(s):  
Shengliang Zhang
Keyword(s):  
Stock Price ◽  
Interpolation Method ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Options Pricing ◽  
Interpolation Scheme ◽  
Time Step ◽  
Order Accuracy ◽  
Tree Approach

A highly accurate radial basis functions (RBFs) quasi-interpolation method for calculating American options prices has been presented by some researchers, which possesses a high order accuracy compared with existing numerical methods. In this study, we show the convergence of the proposed RBFs quasi-interpolation scheme from the view point of probability. It will be confirmed to be a multinomial tree approach, in which in one time step the underlying stock price can arrive at an infinity of possible values. This helps understand the high-order accuracy of the method.

scholarly journals Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Lang Wu ◽  
Dazhi Zhang ◽  
Boying Wu ◽  
Xiong Meng
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Interpolation Scheme ◽  
Numerical Examples ◽  
Weighted Essentially Nonoscillatory ◽  
Accuracy Test ◽  
A Cell ◽  
Fifth Order ◽  
Cell Average ◽  
Essentially Nonoscillatory

Fifth-order mapped semi-Lagrangian weighted essentially nonoscillatory (WENO) methods at certain smooth extrema are developed in this study. The schemes contain the mapped semi-Lagrangian finite volume (M-SL-FV) WENO 5 method and the mapped compact semi-Lagrangian finite difference (M-C-SL-FD) WENO 5 method. The weights in the more common scheme lose accuracy at certain smooth extrema. We introduce mapped weighting to handle the problem. In general, a cell average is applied to construct the M-SL-FV WENO 5 reconstruction, and the M-C-SL-FD WENO 5 interpolation scheme is proposed based on an interpolation approach. An accuracy test and numerical examples are used to demonstrate that the two schemes reduce the loss of accuracy and improve the ability to capture discontinuities.

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