Sökning: "summation by parts"

Visar resultat 1 - 5 av 27 uppsatser innehållade orden summation by parts.

  1. 1. Numerical simulation of the non-linear Schrödinger equation A comparative study based on the summation-by-parts method in space and time

    Master-uppsats, Uppsala universitet/Institutionen för informationsteknologi

    Författare :Ibrohim Hamoud; [2023]
    Nyckelord :;

    Sammanfattning : In this work, we present the numerical implementation of various time marching methods based on the summation-by-parts (SBP) method for the time integration of nonlinear dispersive systems. More specifically, we consider the nonlinear Schrödinger (NLS) equation that accepts soliton or soliton-like solution as a primary case study. LÄS MER

  3. 2. Simulation of low frequency acoustic waves in small rooms : An SBP-SAT approach to solving the time dependent acoustic wave equation in three dimensions

    Kandidat-uppsats,

    Författare :Alva Fährlin; Olle Edgren Schüllerqvist; [2023]
    Nyckelord :room acoustics; numerical methods; SBP; SAT; acoustic wave equation.;

    Sammanfattning : Low frequency acoustic room behaviour can be approximated using numerical methods. Traditionally, music studio control rooms are built with complex geometries, making their eigenmodes difficult to predict mathematically. LÄS MER

  4. 3. Numerical Simulation of the Generalized Modified Benjamin-Bona-Mahony Equation Using SBP-SAT in Time

    Kandidat-uppsats, Uppsala universitet/Avdelningen för beräkningsvetenskap

    Författare :Vilma Kjelldahl; [2023]
    Nyckelord :Benjamin-Bona-Mahony equation; non-linear; initial boundary value problem; summation-by-parts; simultaneous-approximation-term; time integration; simulation;

    Sammanfattning : This paper describes simulations of the generalized modified Benjamin-Bona-Mahony (BBM) equation, using finite difference methods (FDM). Well-posed boundary conditions (BCs) as well as stable semi-discrete approximations are derived using summations-by-parts (SBP) operators combined with the projection method. LÄS MER

  5. 4. Computation of Acoustic Wave Propagation Under Water

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Frida Thörn; [2022]
    Nyckelord :Wave equation; Helmholtz equation; Waveholtz iteration; finite difference method; summation by parts; energy method; point source; curvilinear coordinates; vågekvationen; helmholtz ekvation; waveholtz iteration; finita differens methoden; energimetoden; punktkälla; kurvlinjära koordinater; kroklinjiga koordinater; SBP;

    Sammanfattning : In this thesis we look at acoustic wave propagation under water. We look in particular at waves generated by a point source and what happens with the propagation when we model the bottom as flat or as curvilinear. We assume the source to be working at a certain frequency and therefore we model this problem by solving the Helmholtz equation. LÄS MER

  7. 5. Numerical solutions to the incompressible Navier-Stokes equations : Finite difference solutions in curvilinear coordinates

    Uppsats för yrkesexamina på avancerad nivå, Uppsala universitet/Avdelningen för beräkningsvetenskap

    Författare :David Niemelä; [2022]
    Nyckelord :;

    Sammanfattning : A finite difference scheme for the incompressible Navier-Stokes equations in 2-dimensionalcurvilinear coordinates is derived. The scheme uses high-order Summation-By-Parts operatorsand boundaries are handled by the Projection method. LÄS MER