Scalar and Vector Bases for Periodic Pipe Flow

Modified Jacobi polynomials; Orthonormalization of the modified polynomials; Test function space \(\mathcal {N}_p\) : Scalar fields ; Projected functionals; Bases for the test function space \(\mathcal {N}_p\) ; Discrete Fourier transform w.r.t. the angular coordinate; Scalar parity conditions and design requirementsi and construction of a scalar basis; Same steps for vector bases; Gram-Schmidt orthonormalization; Numerical accuracy checks.