scholarly journals Comparative Study on the Open Boundary Conditions of Shallow Flows

10.29007/pf1g ◽  
2018 ◽  
Author(s):  
Jaeyoung Jung ◽  
Jin Hwan Hwang
Keyword(s):  
Boundary Conditions ◽  
Comparative Study ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Shallow Flows ◽  
Incoming Information ◽  
Physical Phenomena ◽  
Internal Domain

In order to accurately simulate physical phenomena, appropriate boundary conditions must be implemented. Where some information propagate along the characteristic curves as in the hyperbolic system such as shallow water equations (SWEs), open boundary conditions (OBCs) must be designed so that such an event should also be maintained even at the boundaries. In other words, OBCs of SWEs must pass information out of the domain and receive the incoming information without any numerical distortion. If OBCs do not reflect the characteristics of SWE, errors will occur and contaminate the information in the internal domain. This study compares several OBCs based on the hyperbolic characteristics of SWE and shows that OBCs derived using hyperbolic characteristic performs better in the several OBCs.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

Sign in / Sign up

Export Citation Format

Share Document