Hi Alex, I am sorry. I misunderstood your question yesterday. The direct solver I mentioned is for the "GlobalSysSoln" property, such as <I PROPERTY="GlobalSysSoln" VALUE="DirectMultiLevelStaticCond" /> <I PROPERTY="GlobalSysSoln" VALUE="XxtMultiLevelStaticCond" /> Its counterpart is the iterative solver, like "IterativeStaticCond". The direct solver for GlobalSysSoln is for general spectral element problems. The direct solver you said is the "CoupledLinearNS" for the incompressible N-S equation, and its counterpart is the VelocityCorrectionScheme. In the CoupledLinearNS solver, if you use EQTYPE=SteadyLinearisedNS, the equation to be solved is the linearized N-S equation, not its adjoint. The baseflow is defined by <FUNCTION NAME="AdvectionVelocity">. In this situation, the EvolutionOperator = Nonlinear,Direct,Adjoint,SkewSymmetric have the same effect. The adjoint equation of SteadyLinearisedNS has not been implemented in CoupledLinearNS yet. Cheers Ankang ________________________________ From: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> on behalf of Gao, Ankang <ankang.gao@imperial.ac.uk> Sent: 31 July 2021 19:17 To: nektar-users <nektar-users@imperial.ac.uk>; A.P. <k210@list.ru> Subject: Re: [Nektar-users] direct solver adjoint advection? Hi Alex, The direct solver solves the global linear system in the spectral element problem, like A x = b. In the incompressible flow solver, the nonlinear advection term is treated as a part of the right-hand-side term b. So, the direct solver can be used in adjoint advection problems. Cheers Ankang ________________________________ From: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> on behalf of A.P. <k210@list.ru> Sent: 31 July 2021 16:45 To: nektar-users <nektar-users@imperial.ac.uk> Subject: [Nektar-users] direct solver adjoint advection? This email from k210@list.ru originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. Hello, does the direct solver support adjoint advection: <I PROPERTY="SolverType" VALUE="CoupledLinearisedNS" /> <I PROPERTY="EQTYPE" VALUE="SteadyLinearisedNS" /> <I PROPERTY="EvolutionOperator" VALUE="Adjoint" /> Alex Proskurin Altai state technical university