Abstract The paper is dedicated to the memory of one of the founders of numerical modeling in oceanology, A. S. Sarkisyan. Typical problems of general ocean circulation and methods of their numerical solution developed by the Russian school of oceanologists are presented. Attention is given to variational algorithms based on the solution of systems of direct and adjoint equations. Three typical problems of ocean dynamics are considered: a quasi-geostrophic model of barotropic eddy currents in the Southern Ocean, a two-layer baroclinic model, and a complete “primitive” model with assimilation of field data developed at INM RAS. Results of numerical experiments for the model of the dynamics of the Black and Azov Seas are presented.
Abstract A. S. Sarkisyan developed a diagnostic method in the 1960s, based on the inclusion of annual mean temperature and salinity fields in circulation models, which made it possible to simulate climatic currents in the World Ocean and a number of other marine basins. As observations of seawater temperature and salinity accumulated, their climatic seasonal cycle became available on regular grids for several marine areas. Therefore, A. S. Sarkisyan and his followers extended the diagnostic method by proposing a set of algorithms, including nudging, which allowed the simulation of seasonal circulation for any individual marine basin. Recently, the possibility has emerged of using daily eddy-resolving three-dimensional temperature and salinity fields reconstructed from satellite observations on a regular grid. This makes it possible to apply nudging to the reanalysis of the Black Sea state and to off-line field analysis of the World Ocean. Nudging has shown good correspondence with similar results obtained by more complex assimilation schemes. Based on these results and developing the ideas of A. S. Sarkisyan that the key information about ocean currents is contained in the spatial distribution of the density field, an economical algorithm for four-dimensional variational assimilation of temperature and salinity observations in an ocean circulation model is proposed here.
Abstract This study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers, in comparison to the widely used variational method. The Adaptive Neural Network (ANN) filter, proposed in this paper, is sequential and stable even for unstable dynamical systems, with the gain parameters as control variables. This ANN filter is called ANNSEIKF0, being based on the Adaptive Singular Evolutive Interpolated Kalman Filter (ASEIKF0). To deal with the uncertainty of the system parameters and of the noise covariance, the proposed filter ANNSEIKF0 makes use of the covariance of reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in the implementation of this filter is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the NNSEIKF0 (Neural network based on SEIKF0) and the ANNSEIKF0, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between these two filters is given to show the high efficiency of the proposed ANNSEIKF0.
Abstract The paper is focused on numerical analysis of hydrodynamic stability of boundary layers with Falkner–Skan–Cooke and Gaster velocity profiles. It is shown that domains of instability and neutral curves for such flows can self-intersect. A method for sorting eigenvalues and a more general description of instability regions are proposed assuming that solutions may be multivalued.
Abstract A fully coupled finite volume – virtual element discretization scheme for the three-dimensional unsaturated poroelasticity equations is presented. The scheme is applicable to unstructured grids with polyhedral cells. Compared to previous work, the scheme overcomes 𝕂-orthogonality restriction by employing multipoint flux approximation, and is expanded to more complex partially saturated case adopting the Richards approach. Convergence properties and robustness with the respect to mesh types are examined.
Abstract This work focuses on optimizing previously developed variational data assimilation methods for the INM-IM global Earth ionosphere dynamical model to achieve more efficient numerical short-term recovery of the global ionospheric F region characteristics. Several modifications to the existing algorithms are proposed. First, the formulation of the assimilation problem and its implementation are enhanced by introducing an additional control function in the initial conditions. Furthermore, the role of different control types in assimilating ionospheric data is investigated. Finally, a method for splitting the assimilation time interval into subintervals is implemented, which significantly increases the overall computational efficiency of the algorithm while maintaining solution reconstruction accuracy.
Abstract We present a preconditioned conjugate gradient solver with a two-level multiplicative preconditioner for symmetric positive-definite systems arising from finite element discretizations. The method combines a block-Jacobi smoother at the fine level with a smoothed aggregation algebraic multigrid coarse correction. A mixed-precision strategy uses single-precision arithmetic in the preconditioner while maintaining double-precision CG iterations. All solver parameters are determined automatically from the matrix structure, with no problem-specific tuning. Numerical experiments on real-world and synthetic FEM benchmarks demonstrate competitive wall-clock performance relative to a leading commercial solver and robustness across various block sizes, strong anisotropy, and large condition numbers.
The paper suggests local and global random walk algorithms for calculating small particle fluxes to remote boundary regions. It solves a long standing problem known in Monte Carlo methods: estimating probabilities of diffusion particles reaching small boundary regions far from the position of point sources. This problem is solved using a new stochastic method based on a combination of the global Random Walk on Spheres algorithm (RWS) and backward trajectory simulation. The problems were studied in transient setting with mixed Dirichlet and Neumann boundary conditions. A series of numerical experiments is presented, demonstrating the advantage of the developed algorithms over the conventional direct Random Walk on Spheres method.
Computational intensity in large-scale microbial simulations is predominantly associated with resolving substrate advection-diffusion dynamics. The paper develops cellular automata-based techniques for models of substrate diffusion, a discrete framework that offers high computational efficiency and can naturally handle complex geometries. A comparative analysis is conducted for a discrete 2D advection-diffusion model implemented on square, extended-square, and hexagonal cellular automaton lattices. Their accuracy is rigorously verified against reference finite-element solutions. Computational experiments demonstrate that hexagonal-based cellular automata achieve higher accuracy than classical finite-difference-like square lattices, while also enabling more realistic and isotropic simulations in complex microbial systems. This work therefore provides a validated, lattice-specific discretization strategy for diffusion, facilitating its efficient integration into hybrid models of microbial systems.
The paper presents a new ocean boundary layer framework developed for numerical simulation of vertical mixing processes. The framework includes turbulence closures of varying complexity: a prognostic k-epsilon scheme, the Pacanowsky-Philander closure, and its dynamic modification proposed by the authors. The turbulent coefficients for the conditions of neutral stratification depend on surface stress and mixed-layer depth in the modified closure. The framework is validated and tested in idealized and observation-based single-column experiments as a stand-alone model and in global simulations as a library implemented in the INM RAS climate model. In the single-column cases, the dynamic modification produces mixed-layer depth and upper-ocean temperature evolution closer to reference solutions than the standard Pacanowsky-Philander closure and shows reduced sensitivity to vertical resolution. In the CORE-II-forced global simulations, the framework implementation modifies zonal-mean temperature and salinity biases in the upper ocean and reduces the global-mean annual mixed-layer depth error.
A number of modifications of the basic algorithms for constructing a multilevel structure to improve the performance of the algebraic multigrid method for both scalar and point-block systems are considered in this paper. We explore the basic operations of transposing and multiplying sparse matrices, as well as ways to select the maximum independent subset in the graph of strong connections, methods for constructing the prolongation operator, and approaches to aggressive coarsening that reduce the operation complexity of the method. It is shown that the construction of an extended prolongation operator can significantly increase the accuracy of the method, but at the cost of higher operator complexity and longer execution times. This disadvantage can be compensated either by filtering small weights from the prolongation operator, or by using aggressive coarsening. Several approaches to aggressive coarsening are considered. To confirm the conclusions, a number of numerical experiments were performed on a series of matrices from a publicly available collection for problems on progressively refined grids. The method applicability is evaluated on systems derived from adaptively generated grids. Some performance analisys of shared and hybrid memory is provided.
The elastic turbulence effect that occurs in the flow of a polymer solution at low Reynolds numbers and high Weissenberg numbers is studied numerically. A physical model of weakly compressible flow of a polymer solution is constructed, and a hybrid numerical technique for approximating this model is developed. Based on this technique, we present a numerical analysis of the polymer flow in a square computational domain with solid boundaries under the action of a periodic external force (Kolmogorov flow). The spectra of velocity, vorticity, and polymer elongation are constructed.
A new data-driven method for the identification of causal interconnections between climate dynamics in different regions is suggested. It is based on assessing the improvements in the data-driven model prediction skills after inclusion of coupling between the regions. The key step of the method is constructing the optimal joint and isolated models of dynamics in two regions in the form of nonlinear stochastic dynamical systems. Bayesian approach is used for optimizations of the model structure. The method is applied to investigation of interactions of sea surface temperature (SST) anomalies between the Pacific and Indian oceans in the tropics. Both real climate data (ERSST reanalysis) and data from three CMIP-level Earth System Models (ESMs) are analyzed. We reveal a strong impact of the Pacific SST anomalies on the Indian ocean dynamics, especially, Indian Ocean Basin Mode and Indian Ocean Dipole with the time lag of 2-4 months. In the Pacific Ocean, the region of eastern El-Ni & ntilde;o formation is sensitive to the Indian Ocean modes. Regarding the ESMs, our results demonstrate significant distinctions of interbasin connections both between the different models and between the models and reanalysis. Nevertheless, the general properties of interactions are shared across all the models and real data: a stronger and wider impact of interaction in the Indian Ocean and a narrow, equatorial impact in the Pacific Ocean. The suggested approach is recommended as a tool for evaluating the ESM regarding their capabilities in reproducing lagged teleconnections in the climate system.
Summation-by-Parts Finite-Difference (SBP-FD) methods are widely used to construct stable, high-order accurate spatial discretizations for hydrodynamics and continuum mechanics. This article presents a locally mass-conserving and monotonic SBP-FD scheme for a tracer advection equation in the flux form. Our approach reformulates the SBP-FD spatial discretization in a finite-volume manner, expressing it as the difference of fluxes across grid cell interfaces. These fluxes are limited using the Flux-Corrected Transport (FCT) method. The resulting scheme preserves monotonicity in terms of the tracer specific concentration - the ratio of tracer density to dry air density. Achieving this required modifications to the standard FCT limiter operating on tracer density. The proposed numerical scheme is evaluated using a standard suite of test cases relevant to atmospheric modelling, demonstrating accuracy comparable to state-of-the-art methods. For smooth tracer distributions, the scheme demonstrates second-order accuracy in the & ell;2-norm. Strict monotonicity is verified for discontinuous initial conditions and wind fields that severely deform the tracer into thin filaments, including divergent wind fields.
In this paper, a distributed parallel version of algebraic multigrid method is proposed for linear algebraic systems arising from discretization of systems of scalar elliptic equations. The implementation demonstrates good scalability on thousands of cores and surpasses the open source packages HYPRE BoomerAMG and PETSc GAMG in performance on a number of systems. Effective scalable implementations of algorithms in the setup stage of the algebraic multigrid method are considered. The possibility of reducing the number of processors in communicator for coarse systems has been implemented. Variants of cycles of the multigrid method are considered, which make it possible to obtain independence of the number of iterations as the system size increases without losing the scalability of the method. These developments form the basis for further extension of the method for multiphysical problems.
The paper presents a generalization of the well-known method of modelling a continuous argument process based on randomized piecewise constant replenishment of the discrete argument process. It is proposed to additionally summarize the trajectories of a piecewise constant process in the case the distributions of the initial process are infinitely divisible. The behavior of continuous argument processes is studied when the number of terms tends to infinity. The conditions under which the sequence of processes constructed this way weakly converges in the Skorokhod and Lp spaces are presented and the properties of limiting processes are studied. In addition, an algorithm for modelling homogeneous random fields with piecewise constant realizations based on the Palm flows and summation of realizations is proposed.
One of the effective approaches to improve the accuracy of RANS modelling in the case of certain classes of flows is the development of corrections which are terms or multipliers in equations of the turbulence model and depend on local characteristics of the flow. The effectiveness of such corrections is largely determined by the choice of arguments for the correction function. This paper is focused on the development of a methodology for optimal selection of such arguments based on machine learning methods. In this paper, we use a 2-stage hybrid method of feature selection that combines filter and wrapper methods. Three multivariate filter methods (RRreliefF, MIMIC, and mRMR) in combination with sequential forward selection method were considered. Using the results of training a neural network model to improve the accuracy of the Spalart-Allmaras (SA) model in the Bump Flow problem as an example, it was shown that a hybrid method using any of the considered filter methods successfully generates a set of arguments for the correction function from a predefined expanded set. Within the framework of this paper, the hybrid method with MIMIC provided the best results.
The approximation of velocity profiles of a laminar pre-separated three-dimensional boundary layer on a swept wing by model one-parameter Falkner-Skan-Cooke profiles and two-parameter Gaster profiles is studied. It is shown that boundary layer velocity profiles of a swept wing can be approximated fairly accurately by the Gaster profiles up to the three-dimensional separation line. It was found that when approaching the separation line, the Gaster profiles providing the best approximation closely resemble the Falkner-Skan-Cooke profiles. It is proposed to use this property to determine the separation location.
Original numerical matrix algorithms for solving various optimal control problems for linear discrete control systems are proposed. The performance of the proposed algorithms is demonstrated using the example of a well-known model of HIV infection and immune response dynamics. In particular, the problem of generation of the optimal disturbance of a given stable stationary solution with a given accuracy is considered.
