An ideal $I$ on $P(\kappa)$ is said to be $\kappa^+$-saturated if there is no sequence $\langle S_\alpha \mid \alpha<\kappa^+\rangle$ of $I^+$ sets such that $\alpha<\beta<\kappa^+\implies S_\alpha\cap S_\beta\in I$.

Theorem 3.5 in Baumgartner and Taylor, Saturation Properties of Ideals in Generic Extensions II, gives an example of a poset that forces that there are no $\omega_2$-saturated ideals on $\omega_1$ by adding a club subset of $\omega_1$ with finite conditions. Definition 4.2 in Cox and Eskew, Strongly Proper Forcing and Some Problems of Foreman, extends this to regular $\kappa=\mu^+$ with $\mu$ regular, $\mu^{<\mu}=\mu$ with a forcing $\mathbb{P}(\mu,\kappa)$.

Is there a known analogue poset for $\kappa$ inaccessible that forces there to be no $\kappa^+$-saturated ideals in the generic extension by adding a similar sort of club?

I don't believe that $\mathbb{P}(\mu,\kappa)$ as in Cox and Eskew (with $\mu<<\kappa$) will work, since their argument that $\mathbb{P}(\mu,\kappa)$ preserves $\kappa$ doesn't appear to go through for $\kappa>\mu^+$.

An ideal $I$ on $P(\kappa)$ is said to be $\kappa^+$-saturated if there is no sequence $\langle S_\alpha \mid \alpha<\kappa^+\rangle$ of $I^+$ sets such that $\alpha<\beta<\kappa^+\implies S_\alpha\cap S_\beta\in I$.

Theorem 3.5 in Baumgartner and Taylor, Saturation Properties of Ideals in Generic Extensions II, gives an example of a poset that forces that there are no $\omega_2$-saturated ideals on $\omega_1$ by adding a club subset of $\omega_1$ with finite conditions. Definition 4.2 in Cox and Eskew, Strongly Proper Forcing and Some Problems of Foreman, extends this to regular $\kappa=\mu^+$ with $\mu$ regular, $\mu^{<\mu}=\mu$ with a forcing $\mathbb{P}(\mu,\kappa)$.

Is there a known analogue poset for $\kappa$ inaccessible that forces there to be no $\kappa^+$-saturated ideals in the generic extension by adding a similar sort of club?

I don't believe that $\mathbb{P}(\mu,\kappa)$ as in Cox and Eskew (with choice of $\mu<\kappa$) will work, since their argument that $\mathbb{P}(\mu,\kappa)$ preserves $\kappa$ doesn't appear to go through for $\kappa>\mu^+$.