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Questions tagged [conservation]

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0answers
89 views

WENO5 scheme in a staggered grid

I'm trying to use the finite-difference WENO scheme to solve the 2D density conservation law with axial symmetry (coordinates $r,z$): $\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho \vec{v}) = \...
3
votes
1answer
125 views

Numerical Lax-Wendroff scheme order of convergence on Burgers equation

I was suggested to move that question here. The question to be as follows. Statement of the problem Is it possible to achieve the second order of convergence (OOC) of Lax-Wendroff (LxW) scheme ...
4
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0answers
74 views

Conservation in finite element codes [duplicate]

Typical finite volume methods are conservative, because fluxes (of e.g., mass or energy) are always between neighboring cells. Is the same generally true for finite element codes? Do I correctly ...
1
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2answers
153 views

Conservation violation in axisymmetric Diffusion Equation

1d diffusion equation Integrating the diffusion equation, $$ \frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial x^2}, $$ with a constant diffusion coefficient D using forward Euler for ...
1
vote
2answers
75 views

Should energy be conserved in an N-body simulation where particles don't lose energy in collisions?

In an N-body simulation where forces between particles are attractive and particles do not lose energy on colliding with walls or each other, should energy be conserved? How could it be, with total ...
3
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2answers
479 views

Discrete conservation and Finite Element methods

What would be the rigorous mathematical expression of the fact that a conservation law discretized with a Finite Element method with Galerkin discretization does not result in a conservative scheme ?
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0answers
164 views

Spherical Advection Discretization (boundary nodes)

Consider the spherical advection problem: describing the conservation of a property $u$ in a closed spherical domain. $$ \frac{\partial u}{\partial t}+\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^...
0
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1answer
64 views

Conservatives in shock tube

We know shock tube problem will give discontinuous solution of primitive variables ($\rho$, $v$, $p$). Will it give discontinuous result in flux terms? $F =[\rho u, \rho u^2 +p, \rho e_v]^T$. I tried ...
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0answers
152 views

Initial conditions of nbody problem

Note: I have edited the original question to try to be clearer. I'm trying to simulate a gravitational nbody problem with a Barnes-Hut algorithm, in which the bodies start in a homogeneous sphere ...
3
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1answer
128 views

Why do planets move at the wrong speed in my solar system model?

Not 100% sure where this question belongs, since I'm not sure if the problem is code related or not. I've written a program to model the solar system. I am now testing its accuracy. I've checked ...
6
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1answer
1k views

PDE - Conservative form, conservative methods and discrete conservation

I cannot find a reference explaining clearly and rigorously the links between the notions of conservative form for a PDE, a conservative numerical method and discrete conservation. I would be very ...
0
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2answers
148 views

Is it possible to show global conservative properties FEM as it is done in FVM?

I know that in FVM, it is possible to show that a discretisation scheme is conservative by adding the discrete terms over a few control volumes and showing that all terms cancel apart from those ...
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2answers
318 views

significance of energy equation and its conservation

I am interested to know the significance of the energy conservation laws when modelling fluids (or other materials). Am I correct in saying that if energy is conserved then stability is achieved. In ...
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2answers
285 views

Can the conservative form of the advection equation be re-written by replacing the velocity term with an integral over all other points in space?

Suppose I have a 1D advection equation in conservation (divergence) form $\partial_t u(x,t) = -\partial_x [v(x)u(x,t)],$ where $u$ is a conserved quantity in space, and $v$ gives the velocity of the ...
6
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2answers
382 views

How does the L-stability or A-stability of a scheme relate to its ability to preserve a quadratic invariant?

I am working with the simple example of an oscillator: $$(1) \; \; \ddot{u} + u = 0, \; \; u(0) = u_0$$ I know that Forward Euler does not preserve an invariant of the above system: $$(2) \; \; \dot{...
3
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0answers
292 views

Euler Equation Eigensystem with Gravity in the Energy Flux

I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
3
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2answers
359 views

Energy Conservation in Conservation Laws with Source Terms

I'm wondering if anyone can help me understand energy conservation when using conservation law methods (i.e. Riemann solver, High-Resolution Wave-Propagation Methods) with the addition of source terms:...
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3answers
3k views

Conservation of Mass in 1D Advection-Diffusion Equation

My long-term goal is to numerically solve the 1D advection-diffusion equation of the form: $$\frac{\partial u}{\partial t}=\frac{\partial }{\partial x}\left( v(x,t) u+D\frac{\partial u}{\partial x}\...
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0answers
53 views

Energy anomolies in many body simulation

I am trying to simulate the gravitational interaction between many bodies. I am using a direct PP force calculation and a 4th order symplectic integrator with a variable step size. The energy of ...
6
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1answer
136 views

Are there high order symplectic methods for $y'=f(y)$?

Are there high order energy-conserving or symplectic methods for solving $y'=f(y)$?
11
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1answer
1k views

Can the advection equation with variable velocity be conservative?

I am trying to understand the advection equation with variable velocity coefficient a bit better. In particular I don't understand how the equation can be conservative. The advection equation, $$ \...