scholarly journals High-order Nyström discretizations for the solution of integral equation formulations of two-dimensional Helmholtz transmission problems

2015 ◽  
pp. drv010
Author(s):  
Yassine Boubendir ◽  
Catalin Turc ◽  
Víctor Domínguez
Keyword(s):  
Integral Equation ◽  
High Order ◽  
Two Dimensional ◽  
Transmission Problems ◽  
Helmholtz Transmission Problems

scholarly journals A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Meilan Sun ◽  
Chuanqing Gu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Recursive Algorithm ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Initial Value ◽  
Numerical Examples ◽  
Type Approximation

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the initial value, from low to high order, and gradually proceeds. Compared with the original two methods, the numerical examples show that the algorithm is effective.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1080-1081
Author(s):  
Giuseppe Davi ◽  
Rosario M. A. Maretta ◽  
Alberto Milazzo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Element Method

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

High-order quasi–phase-matching harmonic generation in two-dimensional orthorhombic lattice

2004 ◽  
Vol 68 (6) ◽  
pp. 804-810 ◽  
Author(s):  
Boqin Ma ◽  
Ting Wang ◽  
Peigen Ni ◽  
Bingying Cheng ◽  
Daozhong Zhang
Keyword(s):  
Harmonic Generation ◽  
High Order ◽  
Phase Matching ◽  
Two Dimensional ◽  
Orthorhombic Lattice ◽  
Quasi Phase Matching

scholarly journals A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction

2021 ◽  
pp. 105152
Author(s):  
Victor Michel-Dansac ◽  
Christophe Berthon ◽  
Stéphane Clain ◽  
Françoise Foucher
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
Two Dimensional
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