Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Aside from extra computational cost due to having to compute both fluxes over a certain region, is there any downside to blend two flux evaluations for a hybrid scheme in a finite volume method? The flux evaluation would look like this:

$\mathbf{F}_{i+\frac12} = \Lambda_{i+\frac12} \mathbf{F}^c_{i+\frac12} + (1 - \Lambda_{i+\frac12}) \mathbf{F}^u_{i+\frac12}$

The switch is based on a pressure and/or density gradient sensor depending on your application. $\mathbf{F}^c$ is a central scheme (McCormack, compact, ...) and $\mathbf{F}^u$ is an upwind scheme like a flux-difference splitting with a MUSCL reconstruction. Are there any issues in terms of numerics, conservative properties if I am blending the two schemes using a continuous function for $\Lambda$ as opposed to simply switching between schemes with $\Lambda$ valued as either 0 or 1?

share|improve this question
The classic example of switches-gone-wrong is the 1970 Murman-Cole scheme for transonic potential equations (fixed in 1973). If your switch, or blending, doesn't yield a telescoping sum then you violate conservation. It's straight forward to test. – tpg2114 Nov 27 '12 at 19:15
How will you be solving the equations? Implicit (pseudo-)time discretization? Switching could then have a negative effect on the iterative convergence. – chris Nov 29 '12 at 20:06
That would be using an explicit time scheme, either predictor-corrector or some basic Runge-Kutta. – FrenchKheldar Nov 29 '12 at 20:08

The approach you are using will maintain conservation either way. There are other obvious approaches that are not conservative, and can cause problems.

It is possible (and even likely) that you will lose an order of accuracy in the region where you switch, if you examine the local truncation error. But typically this error is localized so that the global error is still of the expected order. So in my experience, you will see essentially the same behavior whether you use a hard switch or a transition region.

I have a manuscript on (more or less) this topic: Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws .

I would be very interested in knowing what you see when trying the two approaches, if it is different from what I'm suggesting.

share|improve this answer
awesome, I was hoping you'd be able to comment on this. – Aron Ahmadia Nov 28 '12 at 21:56
Is there a theoretical way to check, akin to telescoping sums? – tpg2114 Nov 29 '12 at 0:13

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.