scholarly journals The Sedov Blast Wave as a Radial Piston Verification Test

2016 ◽  
Vol 1 (3) ◽  
Author(s):  
Clark Pederson ◽  
Bart Brown ◽  
Nathaniel Morgan
Keyword(s):  
Energy Source ◽  
Boundary Condition ◽  
Point Source ◽  
Blast Wave ◽  
Time Varying ◽  
Initial Condition ◽  
Piston Problem ◽  
Great Utility ◽  
Verification Problem ◽  
Verification Test

The Sedov blast wave is of great utility as a verification problem for hydrodynamic methods. The typical implementation uses an energized cell of finite dimensions to represent the energy point source. This approximation can be avoided by directly finding the effects of the energy source as a boundary condition (BC). The proposed method transforms the Sedov problem into an outward moving radial piston problem with a time-varying velocity. A portion of the mesh adjacent to the origin is removed and the boundaries of this hole are forced with the velocities from the Sedov solution. This verification test is implemented on two types of meshes, and convergence is shown. The results from the typical initial condition (IC) method and the new BC method are compared.

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

Time, direction of

2018 ◽  
Author(s):  
Jos Uffink
Keyword(s):  
Boundary Condition ◽  
General Principle ◽  
Room Temperature ◽  
Hot Water ◽  
Initial Condition ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Time Direction ◽  
James Clerk Maxwell ◽  
Ice Cube

You can pour a tumblerful of water into the sea, but you can never get that same tumblerful of water out again. James Clerk Maxwell gave this as an example of an irreversible process. There are many other homely examples: coffee and milk will mix if stirred, but white coffee does not unmix if stirred in reverse. An ice cube in a glass of hot water will melt, but we never see water at room temperature spontaneously separate into ice and hot water. Physical theories like thermodynamics or hydrodynamics, which codify this type of irreversible phenomenon, do not allow the same kind of behaviour in the forward and backward direction of time. There is thus a striking asymmetry in the two temporal directions. This is usually referred to as the ‘direction of time’ (or ‘time asymmetry’ or ‘anisotropy’ or the ‘arrow of time’). The source of this asymmetry has been sought in various theories of physics, both classical and quantum. Some explanations appeal to some sort of boundary condition, typically an initial condition, which the explanation admits to be, not a law of the theory, but a matter of happenstance. Other explanations advocate some additional general principle about, for example, temporally asymmetric notions of causality or randomness.

scholarly journals On the evolution of solutions of Burgers equation on the positive quarter-plane

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

scholarly journals Estimation of Treatment Effects in Repeated Public Goods Experiments

Econometrics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 43
Author(s):  
Jianning Kong ◽  
Donggyu Sul
Keyword(s):  
Public Goods ◽  
Treatment Effects ◽  
Time Varying ◽  
Initial Condition ◽  
Finite Sample ◽  
Cross Sectional ◽  
Public Goods Experiments ◽  
Voluntary Contribution Mechanism ◽  
Average Contribution ◽  
Cross Sectional Average

This paper provides a new statistical model for repeated voluntary contribution mechanism games. In a repeated public goods experiment, contributions in the first round are cross-sectionally independent simply because subjects are randomly selected. Meanwhile, contributions to a public account over rounds are serially and cross-sectionally correlated. Furthermore, the cross-sectional average of the contributions across subjects usually decreases over rounds. By considering this non-stationary initial condition—the initial contribution has a different distribution from the rest of the contributions—we model statistically the time varying patterns of the average contribution in repeated public goods experiments and then propose a simple but efficient method to test for treatment effects. The suggested method has good finite sample performance and works well in practice.

scholarly journals Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huafei Di ◽  
Yadong Shang
Keyword(s):  
Boundary Condition ◽  
Relaxation Function ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Initial Energy ◽  
Memory Term ◽  
Initial Condition ◽  
Pseudoparabolic Equation ◽  
Pseudoparabolic Equations ◽  
Nonlinear Pseudoparabolic Equation

We consider the nonlinear pseudoparabolic equation with a memory termut-Δu-Δut+∫0tλt-τΔuτdτ=div∇up-2u+u1+α,x∈Ω,t>0, with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions onp,α, and the relaxation functionλ(t), we prove a finite-time blow-up result by using the concavity method.

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