scholarly journals Hydraulic falls under a floating ice plate due to submerged obstructions

2014 ◽  
Vol 745 ◽  
pp. 208-222 ◽  
Author(s):  
C. Page ◽  
E. I. Părău
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Elastic Shell ◽  
Boundary Integral ◽  
Critical Flow ◽  
Two Dimensional ◽  
Cosserat Theory ◽  
Thin Elastic Shell

AbstractSteady two-dimensional nonlinear flexural–gravity hydraulic falls past a submerged obstruction on the bottom of a channel are considered. The fluid is assumed to be ideal and is covered above by a thin ice plate. Cosserat theory is used to model the sheet of ice as a thin elastic shell, and boundary integral equation techniques are then employed to find critical flow solutions. By utilising a second obstruction, solutions with a train of waves trapped between two obstructions are investigated.

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

scholarly journals Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jufeng Wang ◽  
Fengxin Sun ◽  
Ying Xu
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Potential Problems ◽  
Element Free Method ◽  
Error Estimations ◽  
Element Free

The interpolating boundary element-free method (IBEFM) is a direct solution method of the meshless boundary integral equation method, which has high efficiency and accuracy. The IBEFM is developed based on the interpolating moving least-squares (IMLS) method and the boundary integral equation method. Since the shape function of the IMLS method satisfies the interpolation characteristics, the IBEFM can directly and accurately impose the essential boundary conditions, which overcomes the shortcomings of the original boundary element-free method in enforcing the essential boundary approximately. This paper will study the error estimations of the IBEFM for two-dimensional potential problems and the relationship between the errors and the influence radius and the condition number of the coefficient matrix. Two numerical examples are presented to verify the correctness of the theoretical results in this paper.

AN IMPROVED LOCAL BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

2010 ◽  
Vol 02 (02) ◽  
pp. 421-436 ◽  
Author(s):  
BAODONG DAI ◽  
YUMIN CHENG
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Computational Efficiency ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Potential Problems

Combining the local boundary integral equation with the improved moving least-squares (IMLS) approximation, an improved local boundary integral equation (ILBIE) method for two-dimensional potential problems is presented in this paper. In the IMLS approximation, the weighted orthogonal functions are used as basis functions. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation and does not lead to an ill-conditioned equations system. The corresponding formulae of the ILBIE method are obtained. Comparing with the conventional local boundary integral equation (LBIE) method, the ILBIE method is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be implemented directly and easily as in the finite element method. The ILBIE method has greater computational efficiency and precision. Some numerical examples to demonstrate the efficiency of the method are presented in this paper.

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