So, the advection term is non-linear and therefore usually being treated explicitly. Now, there is a confusion of mine.
Consider the case where N-S eqn has been discretized as
(I-L)*u+C_t*u_t=u_t-1/rho * Dx*p, where I is the identity matrix, L is the standard Laplacian operator for momentum space, C_t is the convection term which has been constructed via previous timestep, u_t is the velocity at the previous timestep. Does Rhie-Chow interpolation deals with the coefficients, which is including the convection term or not?
So I want to know is
A=I-L or A=I-L+C_t
Then this leads to the modified explicit convection expression of C_t*u_t+1.
Previously, I was doing with A=I-L and this seems to blow up the solution but had not verified if the wrongdoing was from the numerical coding of mine or the fault of the theory, where the coefficient has not been properly set.
Thank you.
Dear Woohyuk Noh please do recommend my answer if helpful.
Rhie-Chow interpolation is a numerical technique used in computational fluid dynamics (CFD) to handle pressure-velocity coupling in the simulation of fluid flow, particularly in the context of finite volume methods. It's commonly employed in solving the Navier-Stokes equations for incompressible flows. Rhie-Chow interpolation helps ensure that the discretized equations are consistent with the continuity equation and can provide stable and accurate solutions. Here are some tips and insights about Rhie-Chow interpolation:
Rhie-Chow interpolation is a valuable tool for improving the accuracy of CFD simulations in non-orthogonal grids. Understanding its principles and proper implementation can help ensure more reliable and physically accurate results in fluid flow simulations.
Dear Woohyuk Noh please do well to recommend my answer.
Rhie-Chow interpolation is a technique used in computational fluid dynamics (CFD) to solve the problem of pressure-velocity coupling in the numerical simulation of fluid flows. Specifically, it addresses the issue of pressure-velocity decoupling that can occur in non-staggered grid arrangements, such as the collocated grid arrangement. Rhie-Chow interpolation is commonly used in finite volume methods like the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) and SIMPLER (Semi-Implicit Method for Pressure-Linked Equations Revised) algorithms. Here are some tips and insights about Rhie-Chow interpolation:
Implementing Rhie-Chow interpolation correctly can significantly improve the reliability of CFD simulations, especially in scenarios where pressure-velocity coupling is critical for accurate results. However, it's essential to have a good understanding of the underlying principles and to carefully apply the technique within your specific CFD setup.
Tobias Makuochukwu Onyia I appreciate your concern but your answers seem not to be answering my question yet were listing the general facts about this interpolation method. I had asked whether or not to include the advection term of the coefficient matrix to construct Rhie-Chow interpolantion on continuity equation, which is to couple velocity-only differential operating matrix with pressure terms so that it can be solved for the pressure correction. After some time, I had found that "including" advection term do solves the pressure. So, yes I hast to add advection term.
However, I accept your answer to be the best as it is.
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