scholarly journals Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions

2013 ◽  
Vol 234 ◽  
pp. 353-375 ◽  
Author(s):  
Travis C. Fisher ◽  
Mark H. Carpenter ◽  
Jan Nordström ◽  
Nail K. Yamaleev ◽  
Charles Swanson
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Nonlinear Conservation Laws ◽  
Form Theory ◽  
Split Form

ON PARTICLE WEIGHTED METHODS AND SMOOTH PARTICLE HYDRODYNAMICS

1999 ◽  
Vol 09 (02) ◽  
pp. 161-209 ◽  
Author(s):  
J. P. VILA
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Detailed Analysis ◽  
Particle Methods ◽  
Smooth Particle Hydrodynamics ◽  
Sph Method ◽  
Particle Hydrodynamics ◽  
New Ideas ◽  
Particle Approximation

This paper deal with designing of weighted particle approximation of conservation laws. New ideas concerning the use of variable smoothing length, renormalization and the use of Godunov type finite difference fluxes in particle methods are introduced and discussed in connection with standard implementation of the SPH method. A detailed analysis of boundary conditions approximation is also provided.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

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