arXiv subjects

Houwang Tu

Publications and source records attributed to Houwang Tu.

8 recordsLinked to original sources

arXiv2024

Application of a spectral scheme to simulate horizontally slowly varying three-dimensional ocean acoustic propagation

Three-dimensional numerical models for underwater sound propagation are popular in computational ocean acoustics. For horizontally slowly varying waveguide environments, an adiabatic mode-parabolic equation hybrid theory can be used for simulation. This theory employs adiabatic modes in the vertical direction, simplifying the solution of the sound pressure to the solution of horizontal refractive index of vertical modes. The refractive equations in the horizontal direction are further solved by a ``split-step" wide-angle parabolic equation model, following the approach of the ``vertical modes and horizontal parabolic equation". Existing three-dimensional sound propagation models mostly use finite difference methods for discretization, but in recent years, the academic community has proposed new types of sound propagation models based on spectral methods. Spectral methods are numerical discretization methods based on orthogonal polynomial approximation and weighted residual principles. They offer advantages such as high computational accuracy and fast convergence. In this study, a three-dimensional adiabatic mode-parabolic equation hybrid model discretized using spectral methods is proposed. In the vertical direction, the modal functions are solved using the Chebyshev spectral method. The medium layering is handled using a domain decomposition strategy, and the leaky modes under semi-infinite boundary conditions are addressed using an eigenvalue transformation technique. In the horizontal direction, the perfectly matched layer technique is utilized to handle unbounded computational domains, and the perfectly matched layer and computational domain are segmented into multiple layers. Numerical simulations show that the Chebyshev spectral method achieves reliable results in the application of the adiabatic mode-parabolic equation hybrid model.

physics.comp-ph↗

arXiv2023

A Spectral Method for Depth-Separated Solution of a Wavenumber Integration Model in Horizontally Stratified Fluid Acoustic Waveguides

The wavenumber integration model is considered to be the most accurate algorithm for arbitrary horizontally stratified media in computational ocean acoustics. In contrast to the normal mode approach, it considers not only the discrete wavenumber spectrum but also the continuous spectrum components, eliminating errors in the model approximation for horizontally stratified media. Traditionally, analytical and semianalytical methods have been used to solve the depth-separated wave equation in the wavenumber integration method, and numerical solutions have generally focused on the finite difference method and the finite element method. In this paper, an algorithm for solving the depth equation using the Chebyshev--Tau spectral method combined with a domain decomposition strategy is proposed, and a numerical program named WISpec is developed accordingly. The proposed algorithm can simulate not only the sound field excited by a point source but also the sound field excited by an infinite line source. The key idea of the algorithm is to first discretize the depth equations for each layer via the Chebyshev--Tau spectral method and then solve the equations for each layer simultaneously by incorporating boundary and interface conditions. Several representative numerical experiments are devised to test the accuracy and speed of WISpec. The high consistency of the results of different software programs running under the same configuration proves that the numerical algorithm proposed in this paper is accurate, reliable and numerically stable.

math.NA↗

arXiv2022

Application of a Spectral Method to Simulate Quasi-Three-Dimensional Underwater Acoustic Fields

The calculation of a three-dimensional underwater acoustic field has always been a key problem in computational ocean acoustics. Traditionally, this solution is usually obtained by directly solving the acoustic Helmholtz equation using a finite difference or finite element algorithm. Solving the three-dimensional Helmholtz equation directly is computationally expensive. For quasi-three-dimensional problems, the Helmholtz equation can be processed by the integral transformation approach, which can greatly reduce the computational cost. In this paper, a numerical algorithm for a quasi-three-dimensional sound field that combines an integral transformation technique, stepwise coupled modes and a spectral method is designed. The quasi-three-dimensional problem is transformed into a two-dimensional problem using an integral transformation strategy. A stepwise approximation is then used to discretize the range dependence of the two-dimensional problem; this approximation is essentially a physical discretization that further reduces the range-dependent two-dimensional problem to a one-dimensional problem. Finally, the Chebyshev--Tau spectral method is employed to accurately solve the one-dimensional problem. We provide the corresponding numerical program SPEC3D for the proposed algorithm and describe several representative numerical examples. In the numerical experiments, the consistency between SPEC3D and the analytical solution/high-precision finite difference program COACH verifies the reliability and capability of the proposed algorithm. A comparison of running times illustrates that the algorithm proposed in this paper is significantly faster than the full three-dimensional algorithm in terms of computational speed.

physics.comp-ph↗

arXiv2022

A Chebyshev-Tau Spectral Method for Coupled Modes of Underwater Sound Propagation in Range-Dependent Ocean Environments

The stepwise coupled-mode model is a classic approach for solving range-dependent sound propagation problems. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments and numerical instability. In this paper, a new algorithm is designed that uses an improved range normalization and global matrix approach to address range dependence in ocean environments. Due to its high accuracy in solving differential equations, the spectral method has recently been applied to range-independent normal modes and has achieved remarkable results. This algorithm uses the Chebyshev--Tau spectral method to solve for the eigenmodes in the range-independent segments. The main steps of the algorithm are parallelized, so OpenMP multithreading technology is also applied for further acceleration. Based on this algorithm, an efficient program is developed, and numerical simulations verify that this algorithm is reliable, accurate and capable. Compared with the existing coupled-mode programs, the newly developed program is more stable and efficient at comparable accuracies and can solve waveguides in more complex and realistic ocean environments.

physics.comp-ph↗

arXiv2022

A Novel Algorithm to Solve for an Underwater Line Source Sound Field Based on Coupled Modes and a Spectral Method

A high-precision numerical sound field is the basis of underwater target detection, positioning and communication. A line source in a plane is a common type of sound source in computational ocean acoustics. The exciting waveguide in a range-dependent ocean environment is often structurally complicated; however, traditional algorithms often assume that the waveguide has a simple seabed boundary and that the line source is located at a horizontal range of 0 m, although this ideal situation is rarely encountered in the actual ocean. In this paper, a novel algorithm is designed that can solve for the sound field excited by a line source at any position in a range-dependent ocean environment. The proposed algorithm uses the classic stepwise approximation approach to address the range dependence of the environment and uses the Chebyshev--Tau spectral method to solve for the horizontal wavenumbers and modes of approximately range-independent segments. Once the modal information of these flat segments has been obtained, a global matrix is constructed to solve for the coupling coefficients of all segments, and finally, the complete sound field is synthesized. Numerical experiments using a robust numerical program developed based on this algorithm verify the correctness and usability of our novel algorithm and software. Furthermore, a detailed analysis and test of the computational cost of this algorithm show that it is efficient.

physics.comp-ph↗

arXiv2021

Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment

The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the finite difference method (FDM). In this paper, a Legendre collocation method (LCM) based on domain decomposition is proposed to solve this problem. A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of multiple sets of collocation points. The solution process of this method proceeds entirely in physical space, requiring that the original differential equation be strictly established at the collocation points; thus, a dense matrix eigenvalue system is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained. Numerical experiments are presented to demonstrate the validity and applicability of this method. A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM and offers roughly the same accuracy as but a faster calculation speed than other types of spectral methods.

cs.CE↗

arXiv2021

Applying the Chebyshev-Tau spectral method to solve the parabolic equation model of wide-angle rational approximation in ocean acoustics

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the wide-angle rational approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, the correctness of using the CSM discrete PE model in solving the underwater acoustic propagation problem is verified. The test results show that compared with the RAM, the method proposed in this paper can achieve higher accuracy in computational underwater acoustics and requires fewer discrete grid points. After optimization, this method is more advantageous than the FDM in terms of speed. Thus, the CSM provides high-precision reference standards for benchmark examples of the range-independent PE model.

cs.CE↗

arXiv2020

A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment

The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the spectral method has been used for discretization. It is generally more accurate than the finite difference method. However, the spectral method requires that the variables to be solved are continuous in space, and the traditional spectral method is powerless for a layered marine environment. A Chebyshev-Tau spectral method based on domain decomposition is applied to the construction of underwater acoustic normal modes in this paper. In this method, the differential equation is projected onto spectral space from the original physical space with the help of an orthogonal basis of Chebyshev polynomials. A complex matrix eigenvalue / eigenvector problem is thus formed, from which the solution of horizontal wavenumbers and modal functions can be solved. The validity of the acoustic field calculation is tested in comparison with classic programs. The results of analysis and tests show that compared with the classic finite difference method, the proposed Chebyshev-Tau spectral method has the advantage of high computational accuracy. In addition, in terms of running time, our method is faster than the Legendre-Galerkin spectral method.

physics.comp-ph↗