SimVascular / SimVascular/svOneDSolver

Adding outflow term to the solver implementation

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#107 2 comments 0 reactions 2 assignees View on GitHub

@JRao-rgb is already working on this.

Since Nov 7, 2023.

enhancement
Dominant language
C++
Stars
22
Forks
27
PR merge metrics
No merged PRs in 30d

Description

Problem

Currently the implementation of the svOneDSolver implicitly assumes no mass flux along the length of vessels (despite the original formulation including such terms wan02 (1).pdf but not in steele03.pdf).

Strong form with outflow term ($\psi$):
$$\dfrac{\partial S}{\partial t} + \dfrac{\partial Q}{\partial z} = -\psi$$

$$\dfrac{\partial Q}{\partial t} + \dfrac{\partial}{\partial z}((1+\delta)\dfrac{Q}{S}) + \dfrac{S}{\rho}\dfrac{\partial p}{\partial z} = Sf + N \dfrac{Q}{S} + \nu \dfrac{\partial^2 Q}{\partial z^2}$$

Solution

We intend to review the assumptions made during construction of the residual and stiffness matrix to ensure that the outflow term is properly included in the implementation (instead of assuming no net mass flux as is currently done).

Additional context

@mrp089 can you assign both @JRao-rgb and @zasexton to this issue

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