This example uses OpenLayers v10.9.0. The latest is v.
Edit

#### WMS 512x256 Tiles

wms 13 tile 10 non-square 1 grid 8

#####

Example of a WMS layer with a custom grid with 512x256px tiles.

WMS can serve arbitrary tile sizes. This example uses a custom tile grid with non-square tiles.

##### main.js

    import Map from 'ol/Map.js';
    import View from 'ol/View.js';
    import {getWidth} from 'ol/extent.js';
    import TileLayer from 'ol/layer/Tile.js';
    import {get as getProjection} from 'ol/proj.js';
    import OSM from 'ol/source/OSM.js';
    import TileWMS from 'ol/source/TileWMS.js';
    import TileGrid from 'ol/tilegrid/TileGrid.js';

    const projExtent = getProjection('EPSG:3857').getExtent();
    const startResolution = getWidth(projExtent) / 256;
    const resolutions = new Array(22);
    for (let i = 0, ii = resolutions.length; i < ii; ++i) {
      resolutions[i] = startResolution / Math.pow(2, i);
    }
    const tileGrid = new TileGrid({
      extent: [-13884991, 2870341, -7455066, 6338219],
      resolutions: resolutions,
      tileSize: [512, 256],
    });

    const layers = [
      new TileLayer({
        source: new OSM(),
      }),
      new TileLayer({
        source: new TileWMS({
          url: 'https://ahocevar.com/geoserver/wms',
          params: {'LAYERS': 'topp:states', 'TILED': true},
          serverType: 'geoserver',
          tileGrid: tileGrid,
        }),
      }),
    ];
    const map = new Map({
      layers: layers,
      target: 'map',
      view: new View({
        center: [-10997148, 4569099],
        zoom: 4,
      }),
    });

##### index.html

    <!DOCTYPE html>
    <html lang="en">
      <head>
        <meta charset="UTF-8">
        <title>WMS 512x256 Tiles</title>
        <link rel="stylesheet" href="node_modules/ol/ol.css">
        <style>
          .map {
            width: 100%;
            height: 400px;
          }
        </style>
      </head>
      <body>
        <div id="map" class="map"></div>

        <script type="module" src="main.js"></script>
      </body>
    </html>

##### package.json

    {
      "name": "wms-custom-tilegrid-512x256",
      "dependencies": {
        "ol": "10.9.0"
      },
      "devDependencies": {
        "vite": "^3.2.3"
      },
      "scripts": {
        "start": "vite",
        "build": "vite build"
      }
    }