Questions tagged [finite-volume-method]

The tag has no usage guidance.

18 questions
19 views

Implement boundary conditions in finite-volume code for conservation laws

For the numerical solution of scalar hyperbolic conservation laws using finite volume schemes. In order to implement the boundary conditions and the numerical fluxes, make use of Ghost cells. ...
30 views

Find the volume of the cylinder $x^2+y^2\leq 2$ bounded by the xy plane and $z=x^2+y^2$

Find the volume of the cylinder $x^2+y^2\leq 2$ bounded by the xy plane and $z=x^2+y^2$ Not sure how to proceed
13 views

Spline interpolation base on average of function

Let's choose the domain as the unit square and divide it into N^2 subdomain. Now I only know the average of function on each subdomain. I know i can regard the average as the value of the function at ...
18 views

Characteristic lengths of an hexahedron

I am working on an error estimation strategy for a finite element code working on unstructured anisotropic meshes. In order to compute this error estimator I need the characteristic lengths of any ...
78 views

584 views

Solving transport equation with pseudo-spectral and finite volume methods in MATLAB

I have a linear transport equation $$\dot{c}(x; t) + vc_x(x; t) = 0 \tag{1}$$ on an interval $[0; 2π]$ with $v = 1$, periodic boundary conditions and two different initial values $$c(x; 0) = \sin(x)$$...
61 views

What is the advantage to have a locally conservative numerical scheme?

Numerous papers tackle the issue to formulate conservative numerical schemes to solve PDEs. For example Liu, Wang, Zou claim "local mass conservation [...] is a highly preferred property of ...
28 views

advective tem in conservative equation in cylindrical coordinates

A conservative equation for the general property $\phi$ can be written as: $$\frac{D \rho \phi}{Dt}=\nabla\cdot(\Gamma_\phi \nabla\phi)+S_\phi$$ where $\frac{D}{Dt}$ is the material derivative, \$\...
807 views

785 views

Finding the volume-weighted average centroid of a polyhedron

In order to find the centroid of a polyhedral element (for finite volume method) bounded by a set of vertices, we follow the following procedure (from my textbook): 1 - Calculate the geometric centre ...
778 views

Upwind differencing scheme in Finite Volume Method (FVM)

I have some troble in understanding how I can assess the direction of the flow for the upwind differencing scheme. Lets say we have the following ODE: $$a(x)\phi '(x)+b(x)\phi ''(x)=f(x)$$ Now how ...
I'm having a hard time understanding finite volume methods. If I take for example the scalar advection equation $$\partial{u}_{t}+a\partial{u}_{x}=0, a>0$$ with suitable initial and bondary ...